F4 maths problem( Trigonometric )

👨🏻‍🏫 學術台數學

用戶3618

2007-02-02 2:11 am

PQR is a right triangle.POR is a straight line.RSQ is a straight line perpendicular to
the x-axis.OP = 2.5cm, OS = 6cm and RS = 8cm. If OQ is the terminal side of θ,
find sinθ.
Hint:1. The reference angle is in the quadrant Ⅳ.
2.∠RSO is a right angle.
3.∠RQP is also a right angle.

更新1:

唔該大家幫手諗下

回答 (1)

Karin

2007-02-02 6:39 pm

✔ 最佳答案

OR^2 = OS^2 + SR^2
OR^2 = 6^2 + 8^2 = 100
OR = 10

SR/OR = QR/PR = (QS+SR) /(PO+OR)
8/6 = (QS+8)/(2.5+10)
QS = 8.67

OQ^2 = OS^2 + QS^2 = 6^2 + 8.67^2
OQ = 10.54

sinθ = QS/OQ = 8.67/10.54
= 0.82

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