I only have one question # 1 find to the nearest meter the height of a church spire that casts a shadow of 50 meters when the angle of elevation of the sun measures 68 degrees.
tanA = h/X
tan68o = h/50
Solve for h.
124
To find the height of the church spire, we can use the tangent function. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the spire, and the adjacent side is the length of the shadow.
Let's start by finding the height:
Step 1: Convert the angle of elevation from degrees to radians.
To do this, multiply the angle in degrees by π/180.
68 degrees * π/180 = 1.19 radians (rounded to two decimal places)
Step 2: Apply the tangent function.
Using the tangent of 1.19 radians, we have:
tan(1.19) = height / 50m
Step 3: Solve for the height.
Rearrange the equation to solve for the height:
height = tan(1.19) * 50m
Step 4: Calculate the height.
Using a calculator, evaluate the tangent of 1.19 radians:
tan(1.19) ≈ 2.116
Now, plug in the values:
height ≈ 2.116 * 50m
height ≈ 105.8m
Therefore, to the nearest meter, the height of the church spire is approximately 106 meters.
To find the height of the church spire, we can use trigonometry. Here's how you can calculate it step by step:
Step 1: Draw a diagram
Draw a triangle with the church spire, its shadow, and the angle of elevation of the sun as shown. Label the height of the spire as 'h' and the length of the shadow as 's'. The angle of elevation is given as 68 degrees.
Step 2: Identify the trigonometric function to use
Since we know the angle of elevation and the side lengths of the triangle, we can use the tangent function to calculate the height of the spire. The tangent of an angle is equal to the ratio of the opposite side to the adjacent side.
Step 3: Write down the formula
The formula for the tangent function is: tan(angle) = opposite/adjacent.
Step 4: Substitute the values into the formula
tan(68°) = h/s
Step 5: Solve the equation for h
Multiply both sides of the equation by s:
tan(68°) * s = h
Step 6: Calculate the height
Using a calculator, find the tangent of 68 degrees, and multiply it by the length of the shadow (50 meters) to get the height of the church spire:
tan(68°) ≈ 2.548180731
h ≈ 2.548180731 * 50
h ≈ 127.4090366
Therefore, the height of the church spire is approximately 127.41 meters (rounded to the nearest meter).