A Right Triangle Has One Angle That Measures 23 ∘ 23^{\circ} 2 3 ∘ . The Adjacent Leg Measures 27.6 Cm, And The Hypotenuse Measures 30 Cm.What Is The Approximate Area Of The Triangle? Round To The Nearest Tenth.The Area Of A Triangle Is Given By
The area of a triangle is given by
The area of a triangle is a fundamental concept in geometry, and it is essential to understand how to calculate it. The formula for the area of a triangle is given by:
A = (1/2) * b * h
where A is the area of the triangle, b is the base of the triangle, and h is the height of the triangle. However, in the case of a right triangle, we can use the formula:
A = (1/2) * a * b
where a and b are the lengths of the two legs of the right triangle.
Finding the length of the other leg
To find the area of the triangle, we need to find the length of the other leg. We can use the trigonometric function sine to find the length of the other leg. The sine function is defined as:
sin(θ) = opposite side / hypotenuse
In this case, the angle θ is 23°, the adjacent leg is 27.6 cm, and the hypotenuse is 30 cm. We can use the sine function to find the length of the other leg:
sin(23°) = opposite side / 30
opposite side = sin(23°) * 30
opposite side ≈ 0.3907 * 30
opposite side ≈ 11.7221 cm
Calculating the area of the triangle
Now that we have the length of the other leg, we can calculate the area of the triangle using the formula:
A = (1/2) * a * b
where a is the length of the adjacent leg (27.6 cm) and b is the length of the other leg (11.7221 cm).
A = (1/2) * 27.6 * 11.7221
A ≈ 161.4192
Rounding the area to the nearest tenth
The area of the triangle is approximately 161.4192 square centimeters. However, we need to round it to the nearest tenth. Rounding 161.4192 to the nearest tenth gives us:
A ≈ 161.4
Therefore, the approximate area of the triangle is 161.4 square centimeters.
Conclusion
In this article, we discussed how to find the area of a right triangle when one angle is given, and the lengths of the adjacent leg and the hypotenuse are known. We used the trigonometric function sine to find the length of the other leg and then calculated the area of the triangle using the formula A = (1/2) * a * b. We rounded the area to the nearest tenth and found that the approximate area of the triangle is 161.4 square centimeters.
Frequently Asked Questions
- What is the formula for the area of a triangle? The formula for the area of a triangle is A = (1/2) * b * h, where A is the area of the triangle, b is the base of the triangle, and h is the height of the triangle.
- How do I find the length of the other leg of a right triangle? You can use the trigonometric function sine to find the length of the other leg. The sine function is defined as sin(θ) = opposite side / hypotenuse.
- How do I calculate the area of a right triangle? You can use the formula A = (1/2) * a * b, where a and b are the lengths of the two legs of the right triangle.
References
- "Geometry" by Michael S. Artin
- "Trigonometry" by Charles P. McKeague
- "Mathematics for the Nonmathematician" by Morris Kline
The area of a triangle is given by
The area of a triangle is a fundamental concept in geometry, and it is essential to understand how to calculate it. The formula for the area of a triangle is given by:
A = (1/2) * b * h
where A is the area of the triangle, b is the base of the triangle, and h is the height of the triangle. However, in the case of a right triangle, we can use the formula:
A = (1/2) * a * b
where a and b are the lengths of the two legs of the right triangle.
Finding the length of the other leg
To find the area of the triangle, we need to find the length of the other leg. We can use the trigonometric function sine to find the length of the other leg. The sine function is defined as:
sin(θ) = opposite side / hypotenuse
In this case, the angle θ is 23°, the adjacent leg is 27.6 cm, and the hypotenuse is 30 cm. We can use the sine function to find the length of the other leg:
sin(23°) = opposite side / 30
opposite side = sin(23°) * 30
opposite side ≈ 0.3907 * 30
opposite side ≈ 11.7221 cm
Calculating the area of the triangle
Now that we have the length of the other leg, we can calculate the area of the triangle using the formula:
A = (1/2) * a * b
where a is the length of the adjacent leg (27.6 cm) and b is the length of the other leg (11.7221 cm).
A = (1/2) * 27.6 * 11.7221
A ≈ 161.4192
Rounding the area to the nearest tenth
The area of the triangle is approximately 161.4192 square centimeters. However, we need to round it to the nearest tenth. Rounding 161.4192 to the nearest tenth gives us:
A ≈ 161.4
Therefore, the approximate area of the triangle is 161.4 square centimeters.
Conclusion
In this article, we discussed how to find the area of a right triangle when one angle is given, and the lengths of the adjacent leg and the hypotenuse are known. We used the trigonometric function sine to find the length of the other leg and then calculated the area of the triangle using the formula A = (1/2) * a * b. We rounded the area to the nearest tenth and found that the approximate area of the triangle is 161.4 square centimeters.
Frequently Asked Questions
Q: What is the formula for the area of a triangle?
A: The formula for the area of a triangle is A = (1/2) * b * h, where A is the area of the triangle, b is the base of the triangle, and h is the height of the triangle.
Q: How do I find the length of the other leg of a right triangle?
A: You can use the trigonometric function sine to find the length of the other leg. The sine function is defined as sin(θ) = opposite side / hypotenuse.
Q: How do I calculate the area of a right triangle?
A: You can use the formula A = (1/2) * a * b, where a and b are the lengths of the two legs of the right triangle.
Q: What is the relationship between the sine function and the area of a triangle?
A: The sine function is used to find the length of the other leg of a right triangle, which is then used to calculate the area of the triangle.
Q: Can I use the cosine function to find the length of the other leg of a right triangle?
A: No, the cosine function is not used to find the length of the other leg of a right triangle. The sine function is used instead.
Q: How do I round the area of a triangle to the nearest tenth?
A: To round the area of a triangle to the nearest tenth, you need to look at the hundredth place and decide whether to round up or down.
Q: What is the approximate area of the triangle in the given problem?
A: The approximate area of the triangle is 161.4 square centimeters.
References
- "Geometry" by Michael S. Artin
- "Trigonometry" by Charles P. McKeague
- "Mathematics for the Nonmathematician" by Morris Kline