Question

question 5.
a ladder is leaning against a house, forming a right triangle with the ground and the wall. the bottom of the ladder is 3 feet away from the base of the house, and the angle between the ladder and the ground is 60 degrees.
how high does the ladder reach on the wall? round your answer to the nearest foot.
a. 4 ft
b. 5 ft
c. 6 ft
d. 8 ft

Explanation:

Step1: Identify trigonometric ratio

We have a right triangle, with adjacent side (ground) = 3 ft, angle with ground = 60°, and we need the opposite side (height on wall, let's call it \( h \)). Use tangent: \( \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \)

Step2: Substitute values

\( \tan(60^\circ) = \frac{h}{3} \). Since \( \tan(60^\circ) = \sqrt{3} \approx 1.732 \), we get \( h = 3 \times \tan(60^\circ) \)

Step3: Calculate height

\( h = 3 \times \sqrt{3} \approx 3 \times 1.732 = 5.196 \), which rounds to 5 ft.

Answer:

B. 5 ft