One Of The Acute Angle Of A Right Angle Triangle Is 63 Degrees Find The Other Acute Angle​

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Introduction

In this article, we will explore the concept of right-angled triangles and how to find the other acute angle when one of the acute angles is given. A right-angled triangle is a triangle with one angle that is 90 degrees. The other two angles are acute angles, which are less than 90 degrees. We will use the given acute angle of 63 degrees to find the other acute angle.

Understanding the Basics of Right-Angled Triangles

A right-angled triangle has three angles: two acute angles and one right angle. The sum of the measures of the three angles in a triangle is always 180 degrees. Since one of the angles is 90 degrees, the sum of the measures of the other two angles must be 180 - 90 = 90 degrees.

Finding the Other Acute Angle

To find the other acute angle, we can use the fact that the sum of the measures of the two acute angles is 90 degrees. Let's call the given acute angle 63 degrees. We can set up an equation to represent the sum of the measures of the two acute angles:

63 + x = 90

where x is the measure of the other acute angle.

Solving the Equation

To solve for x, we can subtract 63 from both sides of the equation:

x = 90 - 63 x = 27

Therefore, the other acute angle is 27 degrees.

Verifying the Answer

To verify our answer, we can check if the sum of the measures of the two acute angles is indeed 90 degrees:

63 + 27 = 90

Since the sum of the measures of the two acute angles is 90 degrees, our answer is correct.

Conclusion

In this article, we have shown how to find the other acute angle in a right-angled triangle when one of the acute angles is given. We used the fact that the sum of the measures of the two acute angles is 90 degrees to set up an equation and solve for the other acute angle. We verified our answer by checking if the sum of the measures of the two acute angles is indeed 90 degrees.

Real-World Applications

The concept of right-angled triangles and finding the other acute angle has many real-world applications. For example, in architecture, engineers use right-angled triangles to design buildings and bridges. In physics, right-angled triangles are used to calculate distances and velocities. In navigation, right-angled triangles are used to calculate distances and directions.

Common Mistakes to Avoid

When solving for the other acute angle in a right-angled triangle, there are several common mistakes to avoid. One mistake is to assume that the given acute angle is the larger angle. Another mistake is to forget to subtract the given acute angle from 90 degrees to find the other acute angle.

Tips and Tricks

To make solving for the other acute angle easier, here are some tips and tricks:

  • Always remember that the sum of the measures of the two acute angles is 90 degrees.
  • Use a diagram to visualize the triangle and the given acute angle.
  • Set up an equation to represent the sum of the measures of the two acute angles.
  • Solve the equation to find the other acute angle.

Conclusion

Q: What is a right-angled triangle?

A: A right-angled triangle is a triangle with one angle that is 90 degrees. The other two angles are acute angles, which are less than 90 degrees.

Q: How do I find the other acute angle in a right-angled triangle?

A: To find the other acute angle, you can use the fact that the sum of the measures of the two acute angles is 90 degrees. Let's call the given acute angle x. You can set up an equation to represent the sum of the measures of the two acute angles:

x + y = 90

where y is the measure of the other acute angle.

Q: What if I don't know the measure of the given acute angle?

A: If you don't know the measure of the given acute angle, you can use the fact that the sum of the measures of the two acute angles is 90 degrees to find the measure of the other acute angle. Let's say the given acute angle is x. You can set up an equation to represent the sum of the measures of the two acute angles:

x + y = 90

You can then solve for y, which is the measure of the other acute angle.

Q: Can I use a diagram to help me find the other acute angle?

A: Yes, you can use a diagram to help you find the other acute angle. Draw a right-angled triangle with the given acute angle and the right angle. Then, use a protractor or a ruler to measure the angle between the two sides that form the right angle. This will give you the measure of the other acute angle.

Q: What if I make a mistake when solving for the other acute angle?

A: If you make a mistake when solving for the other acute angle, don't worry! Just go back and recheck your work. Make sure you have set up the equation correctly and that you have solved for the correct variable. If you are still having trouble, try using a diagram to help you visualize the problem.

Q: Can I use a calculator to find the other acute angle?

A: Yes, you can use a calculator to find the other acute angle. Simply enter the measure of the given acute angle and the equation x + y = 90 into the calculator. The calculator will then give you the measure of the other acute angle.

Q: What if I have a triangle with two acute angles and one obtuse angle?

A: If you have a triangle with two acute angles and one obtuse angle, you can use the fact that the sum of the measures of the three angles in a triangle is 180 degrees to find the measure of the obtuse angle. Let's say the two acute angles are x and y. You can set up an equation to represent the sum of the measures of the three angles:

x + y + z = 180

where z is the measure of the obtuse angle.

Q: Can I use trigonometry to find the other acute angle?

A: Yes, you can use trigonometry to find the other acute angle. Let's say you have a right-angled triangle with the given acute angle and the right angle. You can use the sine, cosine, or tangent function to find the measure of the other acute angle.

Q: What if I have a triangle with three right angles?

A: If you have a triangle with three right angles, you can use the fact that the sum of the measures of the three angles in a triangle is 180 degrees to find the measure of each angle. Let's say the three right angles are x, y, and z. You can set up an equation to represent the sum of the measures of the three angles:

x + y + z = 180

Since each angle is a right angle, you know that x = y = z = 90 degrees. You can then solve for the measure of each angle.

Conclusion

In conclusion, finding the other acute angle in a right-angled triangle is a simple process that involves using the fact that the sum of the measures of the two acute angles is 90 degrees. By setting up an equation and solving for the other acute angle, we can find the measure of the other acute angle. With practice and patience, anyone can become proficient in solving for the other acute angle in a right-angled triangle.