Question

q.13 solve a right triangle gpr
solve the right triangle.
write your answers as integers or as decimals rounded to the nearest tenth.
$rs = $
$rt = $
$m\angle s = \square ^\circ$
submit
work it out

Explanation:

Step1: Find $m\angle S$

Sum of angles in $\triangle=180^\circ$
$m\angle S = 180^\circ - 90^\circ - 49^\circ = 41^\circ$

Step2: Calculate $RS$ (opposite $\angle T$)

Use sine function: $\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$
$\sin(49^\circ)=\frac{RS}{4} \implies RS = 4\times\sin(49^\circ) \approx 4\times0.7547 \approx 3.0$

Step3: Calculate $RT$ (adjacent to $\angle T$)

Use cosine function: $\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}$
$\cos(49^\circ)=\frac{RT}{4} \implies RT = 4\times\cos(49^\circ) \approx 4\times0.6561 \approx 2.6$

Answer:

$RS \approx 3.0$, $RT \approx 2.6$, $m\angle S = 41^\circ$