The measure of an angle is 29.1°. What is the measure of its complementary angle?
2 answers:
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Answer:
x ≈ 8.99
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the relationship between trig functions and sides in a right triangle. Here, the geometry of the problem can be modeled by a right triangle. We are given one side and want to find the difference in lengths of the other side for two different angles.
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<h3>setup</h3>The tower height is the side opposite the angle of elevation. The distance from the tower to the end of the shadow is the side adjacent to the angle of elevation, so the relevant trig relation is ...
Tan = Opposite/Adjacent
tan(angle of elevation) = (tower height)/(length of shadow)
Solving for the length of shadow, we have ...
length of shadow = (tower height)/tan(angle of elevation)
The difference in shadow lengths is 2x for the two different angles, so we have ...
2x = 24.57/tan(30°) -24.57/tan(45°)
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<h3>solution</h3>Dividing by 2 and factoring out the tower height, we have ...
x = 12.285(1/tan(30°) -1/tan(45°)) = 12.285(√3 -1)
x ≈ 8.993244
The value of x is about 8.99.
Answer:
52.33% is the correct answer.
Step-by-step explanation:
<u>Given that:</u>
Area of triangle = 24 sq units
Center of Circle is at <em>(0, 0)</em> and the circle passes through <em>(1.2, 1.6).</em>
<u>To find:</u> The percentage of triangle covered by circle.
<u>Solution:</u> To find the required percentage, we need to find the area of circle.
To find the area of circle, we need the radius of circle.
Radius of circle is the distance between the center of circle and any point that lies on the periphery of the circle.
We can use Distance formula :
Radius =
Now, area of circle is given by the formula:
Area =
Area = 3.14 = 12.56 sq units
Percentage of Triangle covered:
Hence, 52.33% is the correct answer.