Question

end-of-unit 7 review: right triangle trigonometry 1. what is the length of the altitude, segment cd, of triangle abc? a. $7\sqrt{3}$ square units b. $14\sqrt{3}$ square units c. $14\sqrt{2}$ square units d. $7\sqrt{2}$ square units (image of triangle abc with angle at a being 30°, angle at b being 60°, side bc is 14, and cd is the altitude from c to ab, forming right angles at d.)

Explanation:

Step1: Identify triangle BCD properties

In right $\triangle BCD$, $\angle B = 60^\circ$, hypotenuse $BC=14$. Let $CD = h$ (altitude).
$\sin(60^\circ) = \frac{h}{BC}$

Step2: Solve for h

Substitute values: $h = BC \cdot \sin(60^\circ) = 14 \cdot \frac{\sqrt{3}}{2}$
Simplify: $h = 7\sqrt{3}$

Answer:

a. $7\sqrt{3}$ square units