Question

(someone please answer these. im literally not turning in my test until someone does. ) 1 a ladder is leaning agisnt a building so that the top of the ladder is touching the roof line. the bottom of the ladder is 8 feet from thr building and thr ladder is 17 feet long. how far is the roof line from the ground 15 ft, 9ft 18.8 ft 25ft

2 what is the value of x ?

Answer 1

Answer:

1. 15ft

2. 12

Step-by-step explanation:

1. See the attachment below showing the right triangle formed by the ladder and the building.

Let x represent how far the roof line is from the ground.

Thus, using Pythagorean Theorem, x can be solved as follows:

x² = 17² - 8²

x² = 225

x = √225

x = 15ft

2. Given:

Reference angle = 45°

x = Hyp

6√2 = opposite

Using trigonometric ratios formula, thus:

$sin(45) = \frac{6\sqrt{2}}{x}$

Multiply both sides by x

$sin(45)*x = 6\sqrt{2}$

Divide both sides by sin(45)

$x = \frac{6\sqrt{2}}{sin(45)}$

$x = \frac{6\sqrt{2}}{\frac{1}{\sqrt{2}}}$ (common value of sin(45) = 1/√2)

$x = 6\sqrt{2} \times \frac{\sqrt{2}}{1}$

$x = 6\sqrt{2 \times 2}$

$x = 6 \times 2$

$x = 12$