Question

Pleas help me in this question Find R

Answer 1

`\boxed {\boxed {\sf D. \ 25.8 \textdegree} }`

Explanation:

We are asked to find the measure of an angle given the triangle with 2 sides. This is a right triangle because of the small square representing a right angle. Therefore, we can use trigonometric functions. The three major functions are:

• sinθ= opposite/hypotenuse
• cosθ= adjacent/hypotenuse
• tanθ= opposite/adjacent

We are solving for angle R, and we have the sides TR (measures 9) and SR (measures 10).

• The side TR (9) is adjacent or next to angle R.
• The side SR (10) is the hypotenuse because it is opposite the right angle.

We have the adjacent side and the hypotenuse, so we will use the cosine function.

`cos \theta = \frac {adjacent}{hypotenuse}`

`cos R = \frac {9}{10}`

Since we are solving for an angle, we must take the inverse cosine of both sides.

`cos^(-1)(cos R) = cos ^(-1) ( (9)/(10))`

`R = cos ^(-1) ( (9)/(10))`

`R= 25.84193276`

If we round to the nearest tenth, the 4 in the hundredth place tells us to leave the 8 in the tenths place.

`R \approx 25.8 \textdegree`

The measure of angle R is approximately 25.8 degrees and choice D is correct.

Answer 2

R = 25.8

Explanation:

Since this is a right triangle, we can use trig functions

cos R = adj side / hyp

cos R = 9/10

Taking the inverse cos of each side

cos ^-1 ( cos R) = cos^ -1 ( 9/10)

R=25.84193

Rounding to the nearest tenth

R = 25.8