Question

Solve the right triangle.(Hint: Find all missing sides and angles)

Answer 1

• BC = 7√5 units.

,

• m∠B=41.8°

,

• m∠C=48.2°

Explanation:

First, find the length of the third side, BC using the Pythagorean theorem.

`\begin{gathered} AB^2=AC^2+BC^2 \\ 21^2=14^2+BC^2 \\ BC^2=21^2-14^2 \\ BC=√(21^2-14^2) \\ BC=√(245) \\ BC=√(49*5) \\ BC=7√(5) \end{gathered}`

The length of the third side, BC is 7√5 units.

(b)Next, find the measure of angle B.

• The side length ,opposite, B = 14

,

• The length of the ,hypotenuse, = 21

From trigonometric ratios:

`\begin{gathered} \sin B=(Opposite)/(Hypotenuse) \\ \sin B=(14)/(21) \\ T\text{ake the arcsine of both sides:} \\ B=\arcsin((14)/(21)) \\ B\approx41.8\degree \end{gathered}`

The measure of angle B is 41.8 degrees.

(c)Finally, find the measure of angle C.

In a right triangle, the sum of the two acute angles is 90 degrees, therefore:

The measure of angle C is 48.2 degrees.