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In △PQR, find the measure of ∡P. Triangle PQR where angle Q is a right angle. QR measures 33 point...
10 months ago
Q:
In △PQR, find the measure of ∡P. Triangle PQR where angle Q is a right angle. QR measures 33 point 8. PR measures 57 point 6. Measure of angle P is unknown.
Accepted Solution
A:
Answer: " m∠P = 35.9306 ° " .
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Explanation:
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Given the following right triangle:
P
|
| \
| \
| \
| \
| \ 57.6
| \
| \
| \
|-- \
|_|___________\
Q 33.8 R
Solve for: " m∠P ";
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Using "SOH -CAH- TOA" mnemonic;
Use "SOH" : sine = opposite/ hypotenue ;
→ sin (m∠P) = (33.8) / (57.6) ;
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→ (33.8) / (57.6) = 0.5868055555555556 ;
→ sin (m∠P) = 0.5868055555555556 ;
Take the "arcsin" of each side of the equation;
to find the: "m∠P" ;
→ arcsin [sin m∠P] = arcsin (0.5868055555555556) ;
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→ m∠P = 35.930646907667 ° ; → round to: " 35.9306 ° " .
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