Find the area of triangle ABC.

Given:
\[ C = 134.9^\circ \]
\[ a = 47.8 \, \text{ft} \]
\[ b = 38.2 \, \text{ft} \]

Question

01-06-2024
Mathematics

High School

Thank you for visiting Find the area of triangle ABC Given C 134 9 circ a 47 8 text ft b 38 2 text ft. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!

Find the area of triangle ABC.

Given:
\[ C = 134.9^\circ \]
\[ a = 47.8 \, \text{ft} \]
\[ b = 38.2 \, \text{ft} \]

Answer :

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adrshrivastav78 adrshrivastav78 · Answer 1 · 2024-09-01T17:49:14-04:00

The area of triangle ABC is approximately 1190.25 square feet. To find the area of triangle ABC, we can use the formula for the area of a triangle: A = 1/2 * base * height.

Step 1: Find the height of the triangle.
We can use the Law of Sines to find the height. The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant. In this case, we have angle C and sides a and b.

First, we find the third angle of the triangle:
Angle A + Angle B + Angle C = 180°
Angle A + 90° + 134.9° = 180°
Angle A = 180° - 90° - 134.9°
Angle A = 45.1°

Now, we can use the Law of Sines to find the height:
sin(45.1°) / 47.8ft = sin(134.9°) / h
h = (47.8ft * sin(134.9°)) / sin(45.1°)
h ≈ 62.47ft

Step 2: Calculate the area of the triangle.
Using the formula A = 1/2 * base * height, where the base is side b and the height is h:
A = 1/2 * 38.2ft * 62.47ft
A ≈ 1190.25ft²

To know more about Law of Sines visit:

https://brainly.com/question/21634338

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Find the area of triangle ABC.Given:\[ C = 134.9^\circ \]\[ a = 47.8 \, \text{ft} \]\[ b = 38.2 \, \text{ft} \]

Answer :

Other Questions

Find the area of triangle ABC.

Given:
\[ C = 134.9^\circ \]
\[ a = 47.8 \, \text{ft} \]
\[ b = 38.2 \, \text{ft} \]