Answer to Question #266321 in Trigonometry for Snd

Question

A 12-ft ramp rests against the edge of the floor at the back door of a truck. To make it

stable 2.5 ft of the ramp extends beyond the edge of the floor, which is 3.5 ft above the

level ground. Find the tangent and the cosine of the angle that makes with the ground.

Answer 1

Given

$$|BD|=12\ ft$$

$$|AD|=2.5\ ft$$

$$|AC|=3.5\ ft$$

Then

$$|AB|=|BD|-|AD|=12-2.5=9.5(ft)$$

Use the Pythagorean Theorem

$$|AB|^2=|AC|^2+|BC|^2$$

$$|BC|=\sqrt{|AB|^2-|AC|^2}$$

$$=\sqrt{9.5^2-3.5^2}=\sqrt{78}(ft)$$

$$\tan \theta=\dfrac{|AC|}{|BC|}=\dfrac{3.5}{\sqrt{78}}\approx0.396297$$

$$\cos \theta=\dfrac{|BC|}{|AB|}=\dfrac{\sqrt{78}}{9.5}\approx0.929659$$