Answer:
Measure of [tex]\angle P[/tex] to nearest tenth of a degree is [tex]47.5^{\circ}[/tex].
Step-by-step explanation:
Diagram of given scenario is shown below.
Given that,
A right angle triangle [tex]\triangle OPQ[/tex]. Base of triangle is [tex]QP[/tex].
Perpendicular side of triangle is [tex]OQ[/tex] and Hypotenuse side of triangle is [tex]OP[/tex].
In [tex]\triangle OPQ[/tex], [tex]\angle Q=90^{\circ}[/tex],[tex]QO=5.9[/tex] and [tex]OP=8[/tex].
Now, Using Trigonometry ratio:
[tex]Sin\theta=\frac{Perpendicular}{Hypoteneuse}[/tex]
So, Substituting the values of perpendicular and hypotenuse we get:
[tex]Sin\angle P = \frac{OQ}{OP} =\frac{5.9}{8}[/tex]
[tex]Sin\angle P = 0.7375[/tex] ⇒ [tex]\angle P= Sin^{-1}(0.7375)=47.51888^{\circ}[/tex]
Therefore, Measure of [tex]\angle P[/tex] to nearest tenth of a degree is [tex]47.5^{\circ}[/tex].
Answer:
47.5°
Step-by-step explanation:
\sin P =
hypotenuse
opposite
= 5.9/8
sin P= 5.9/8
P=sin -1
(5.9/8)
P=47.5189 ≈ 47.5°
