In triangle pqr, we have measure angle p = 90°, pq= 15, and qr = 25.
a. Find sin (angle q) and cos (angle r) .
Answers
ANSWER:—
Hey mate !!
Here's the answer !!
Refer to the attachment for the diagram !!
Given that PQ = 7 cm, PR = 25 cm, ∠ Q = 90°.
Since it is a right angled triangle, we can find the other side of the triangle using Pythagoras Theorem.
In Δ PQR, PQ = Opposite side, PR = Hypotenuse, QR = Adjacent side.
Applying Pythagoras Theorem we get,
=> PR² = PQ² + QR²
=> PR² - PQ² = QR²
=> 25² - 7² = QR²
=> 625 - 49 = QR²
=> 576 = QR²
=> QR = √ 576
=> QR = 24 cm
Hence QR = 24 cm.
So Tan P = Opposite / Adjacent
Opposite side of ∠ P = QR, Adjacent side for ∠ P = PQ.
=> Tan P = QR / PQ
=> Tan P = 24 / 7
Tan R = Opposite / Adjacenet
Opposite side for ∠ R = PQ, Adjacent side for ∠ R = QR.
=> Tan R = PQ / QR
=> Tan R = 7 / 24
So Tan P - Tan R is,
=> 24 / 7 - 7 / 24
=> 3.42 - 0.29
=> 3.13
Hope my answer helped !!
Cheers !!
thanks
hope this helps
