Answer to Question #280146 in Algebra for Idk

Question

His 13- foot ladder leans against the building at a point that is 11.3 feet above the ground.

At what height would a 15-foot ladder touch the building if both ladders form the same angle with the ground? Round your answer to the nearest tenth.

____________ feet

A 15-foot ladder leaning up against a wall at the same angle as the 13-foot ladder would touch the wall at _______ feet.

Explain how you determined your answer (explain all work used to determine the answer).

Find the angle that the 15-foot ladder makes with the building. Round your answer to the nearest tenth. ____________ degrees

Answer 1

$$\sin \alpha=\dfrac{h}{l}=\dfrac{H}{L}=>H=\dfrac{L}{l}\cdot h$$

$$H=\dfrac{15}{13}\cdot 11.3\approx13.0\ (ft)$$

13.0 feet.

A 15-foot ladder leaning up against a wall at the same angle as the 13-foot ladder would touch the wall at $13.0$ feet.

$$\cos \beta=\dfrac{11.3}{13}, 0<\alpha<90\degree$$

$$\beta=\cos^{-1}(11.3/30)\approx29.6\degree$$

The angle that the 15-foot ladder makes with the building is $29.6\degree.$