Final Trusses

Triangle ABC is a right triangle. The length of segment 𝐴𝐵 is 2.5 feet, and the 𝑚∠𝐴=42°.

The length of segment 𝐴𝐶 is

• About 3.36 feet.

• About 3.45 feet.

• About 4.15 feet.

Triangle ABC is a right triangle. The length of segment 𝐴𝐵 is 2.5 feet, and the 𝑚∠𝐴=42°.

Find the length of segment 𝐵𝐶.

• About 2.45 feet.

• About 2.25 feet.

• About 3.15 feet.

• About 3.25 feet.

Triangle DEF is a right triangle, where 𝐷𝐸=10 feet and 𝐷𝐹=15 feet.

Find 𝑚∠𝐷𝐹𝐸.

Answer explanation

The measure of angle DFE is about 41.81°.

Triangle DEF is a right triangle, where 𝐷𝐸=10 feet and 𝐷𝐹=15 feet.

Find 𝑚∠𝐹𝐷𝐸.

• The measure of angle FDE is about 45.19°.

• The measure of angle FDE is about 49.19°.

• The measure of angle FDE is about 48.19°.

• The measure of angle FDE is about 46.19°.

Imagine a house truss with a right triangle. The vertical beam supporting the roof is 6.8 feet tall. The angle between the vertical beam and the sloping diagonal beam is designed to shed rain effectively. However, the exact angle is missing from the blueprints!

If the horizontal beam at the base of the triangle measures 7.5 feet, what trigonometric ratio can we use to find the missing angle between the vertical beam and the diagonal beam?

Answer explanation

We can use the inverse tangent function because we know the opposite side and the adjacent side and need to solve for the angle.

Imagine a house truss with a right triangle. The vertical beam supporting the roof is 6.8 feet tall. The angle between the vertical beam and the sloping diagonal beam is designed to shed rain effectively. However, the exact angle is missing from the blueprints!

Set up the equation and solve for the angle.

Answer explanation

The measure of the angle is approximately 47.8°.