What is the value of x in the right triangle below? If needed, round your answer to two decimal places. 32 angle, 15 inches.
A 10-foot ladder is leaning up against the side of a building so that the top of the ladder reaches the top of the building. If the ladder meets the building at a 32 angle, then what is the height of the building? If needed, round your answer to two decimal places.
cos 32 = h/10
h = 10 cos 32
8.48 feet
To find the value of x in the right triangle, we can use the trigonometric function tangent (tan). In this case, we have the angle of 32 degrees and the opposite side as x.
Using the definition of tangent, we have:
tan(θ) = opposite/adjacent
where θ is the angle and opposite is the side opposite to the angle.
So, we can write the equation as:
tan(32) = x/15
Now, let's solve for x using this equation.
First, let's calculate the value of tan(32) using a calculator or online resources, which is approximately 0.62487.
Now, substituting the values in the equation:
0.62487 = x/15
To isolate x, we can cross-multiply:
0.62487 * 15 = x
Calculating this product, we get:
9.37305 = x
Therefore, the value of x in the right triangle is approximately 9.37 inches.
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To find the height of the building, we can use the trigonometric function sine (sin). In this case, we have the angle of 32 degrees and the ladder length as the hypotenuse.
Using the definition of sine, we have:
sin(θ) = opposite/hypotenuse
where θ is the angle and opposite is the side opposite to the angle.
In this scenario, the opposite side is the height of the building, and the hypotenuse is the length of the ladder (10 feet or approximately 120 inches).
So, we can write the equation as:
sin(32) = height/120
Let's solve for the height of the building using this equation.
First, calculate the value of sin(32) using a calculator or online resources, which is approximately 0.52992.
Now, substituting the values in the equation:
0.52992 = height/120
To isolate height, we can cross-multiply:
0.52992 * 120 = height
Calculating this product, we get:
63.5904 = height
Therefore, the height of the building is approximately 63.59 feet.