Question

HELP ME PLEASE solve the right triangle

Answer 1

ST = 7.2

RT = 4.04

m∠S = 34°

Solution:

Given ΔRST is a right triangle.

RS = 6, ∠T = 56°

$\csc A=\frac{\text {Hypotenuse} }{\text {Opposite side}}$

$\csc A=\frac{ST}{RS}$

$\csc 56^\circ=\frac{ST}{6}$

$\csc 56^\circ \times 6=ST$

1.206 × 6 = ST

7.236 = ST

ST = 7.2

$\cot A=\frac{\text {Adjacent side} }{\text {Opposite side}}$

$\cot A=\frac{RT}{RS}$

$\cot 56^\circ=\frac{RT}{6}$

$\cot 56^\circ \times 6=RT$

0.674 × 6 = RT

4.044 = RT

RT = 4.04

To find the measure of angle S.

Sum of the interior angles of the triangle = 180°

m∠R + m∠S + m∠T = 180°

90° + m∠S + 56° = 180°

m∠S + 146° = 180°

m∠S = 180° – 146°

m∠S = 34°