Question

Given: ∆ABC, CD ⊥ AB, AC = BC, Area of ABC = 32 cm2, m∠A = 72°

Find: CD

Answer 1

Answer:

9.92 cm

Step-by-step explanation:

Given: ∆ABC,

CD ⊥ AB,

AC = BC,

Area of ABC = 32 cm2,

m∠A = 72°

Find: CD

Solution:

Triangle ABC is isosceles triangle with base AB, because AC = BC. In isosceles triangle angles adjacent to the base are congruent. So,

$m\angle A=m\angle B=72^{\circ}$

The sum of the measures of all interior angles is 180°, thus

$m\angle C=180^{\circ}-m\angle A-m\angle B\\ \\m\angle C=180^{\circ}-72^{\circ}-72^{\circ}=36^{\circ}$

The area of the triangle ABC is

$A_{ABC}=\dfrac{1}{2}AC\cdot BC\cdot \sin \angle C\\ \\32=\dfrac{1}{2}AC^2\sin 36^{\circ}\\ \\AC^2=\dfrac{64}{\sin 36^{\circ}}\\ \\AC\approx 10.43\ cm$

Consider right triangle ACD. In this triangle,

$\sin \angle A=\dfrac{CD}{AC}\\ \\\sin 72^{\circ}=\dfrac{CD}{10.43}\\ \\CD=10.43\sin 72^{\circ}\approx 9.92\ cm$

Answer 2

Answer:

9.92 cm

Step-by-step explanation:

Using Trig functions, we can calculate the lengths.