Question

What is the measure of ∠R ? Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth. m∠R= ° A right triangle R S T. Angle S is marked as a right angle. Side R T is labeled as 40 centimeters. Side S T is labeled as 30 centimeters.

Answer 1

48.59

Explanation:

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Answer 2

We have been given that in triangle RST, angle S is marked as a right angle. Side RT is labeled as 40 centimeters. Side ST is labeled as 30 centimeters. We are asked to find the measure of angle R.

First of all, we will draw a right triangle using our given information as shown in the attachment.

We can see that RT is hypotenuse and St is opposite side to angle R. We know that sine relates opposite side to hypotenuse of right triangle.

`\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}`

`\text{sin}(\angle R)=(ST)/(RT)`

`\text{sin}(\angle R)=(30)/(40)`

`\text{sin}(\angle R)=(3)/(4)`

Now, we will use arcsin to solve for angle R as:

`\angle R=\text{sin}^(-1)((3)/(4))`

`\angle R=48.59037789`

Upon rounding to nearest hundredth, we will get:

`\angle R\approx 48.59`

Therefore, the measure of angle R is approximately 48.59 degrees.