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The length of PR is 4.4 units.
Explanation:
It is given that the length of the hypotenuse is 10 units.
Also, the angle of R is 64°
To find the length of PR, we shall use the cosine formula,
Here, , adj = PR and hyp = 10
Substituting these values in the formula, we get,
Multiplying both sides by 10, we get,
Substituting the value for cos 64, we get,
Multiplying, we have,
Rounding off, we get,
Thus, the length of PR is 4.4 units.
Given:
θ = 60°
Radius = 8 in
To find:
The area of the shaded segment.
Solution:
Vertically opposite angles are congruent.
Angle for the shaded segment = 60°
<u>Area of the sector:</u>
A = 33.5 in²
Area of the sector = 33.5 in²
<u>Area of triangle:</u>
A = 32 in²
Area of the triangle = 32 in²
Area of segment = Area of sector - Area of triangle
= 33.5 in² - 32 in²
= 1.5 in²
The area of the shaded segment is 1.5 square inches.