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What is measure of angle R?

Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.

What is measure of angle P?

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What is measure of angle R Enter your answer as a decimal in the box Round only your final answer to the nearest hundredth What is measure of angle P Enter your class=

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aachen

Given is a Right triangle PQR with angle Q = 90 degrees.

Given are sides PQ = 8 cm, QR = 15 cm, PR = 17 cm.

Side PR is the hypotenuse.

We can use formula for "sin" given as follows :-

[tex] sin(\theta)=\frac{Opposite}{Hypotenuse} [/tex]

For angle R, opposite side would be PQ.

[tex] sin(R)=\frac{PQ}{PR} \\\\
sin(R)=\frac{8}{17} \\\\
sin(R)=0.470588235 \\\\
R=sin^{-1}(0.470588235) \\\\
R = 28.07248694 \;\;degrees \approx 28.07 \;degrees [/tex]

For angle P, opposite side would be QR.

[tex] sin(P)=\frac{QR}{PR} \\\\
sin(P)=\frac{15}{17} \\\\
sin(P)=0.882352941 \\\\
P=sin^{-1}(0.882352941) \\\\
P = 61.92751306 \;\;degrees \approx 61.93 \;degrees [/tex]

Hence, R = 28.07 degrees and P = 61.93 degrees.

To solve the problem we must know about Trigonometric functions.

Trigonometric functions

[tex]\rm {Sin \theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]

[tex]\rm {Cos \theta=\dfrac{Base}{Hypotenuse}[/tex]

[tex]\rm {tan\theta=\dfrac{Perpendicular}{Base}[/tex]

where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.

  1. The value of the ∠R is 28.0724°.
  2. The value of the ∠P is 61.9275°.

Given to us

  • PR = 17 cm
  • QR = 15 cm
  • PQ = 8 cm

1. For ∠R

For ∠R, the opposite side will be PR, therefore, PR will be the Perpendicular,

Substituting the values in the formula of Sine,

[tex]\rm {Sin (\angle R)=\dfrac{PQ}{PR}\\\\ [/tex]

[tex]\rm {Sin (\angle R)=\dfrac{8}{17}\\ [/tex]

[tex]\rm {(\angle R)=Sin^{-1} \dfrac{8}{17}\\ [/tex]

[tex]\rm {(\angle R)=28.0724^o [/tex]

Hence, the value of the ∠R is 28.0724°.

2. For ∠P

For ∠P, the opposite side will be QR, therefore, QR will be the Perpendicular,

Substituting the values in the formula of Sine,

[tex]\rm {Sin (\angle P)=\dfrac{QR}{PR}\\\\ [/tex]

[tex]\rm {Sin (\angle P)=\dfrac{15}{17}\\ [/tex]

[tex]\rm {(\angle P)=Sin^{-1} \dfrac{15}{17}\\ [/tex]

[tex]\rm {(\angle R)=61.9275^o [/tex]

Hence, the value of the ∠P is 61.9275°.

Learn more about Sine function:

https://brainly.com/question/6826226

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