From a point 200 yards from the foot of a building, the angle of elevation to the top of the building is 37 degrees.
Find the measure of the angles of the triangle formed by the building, the ground, and the line of sight to the top of the building?
Isn't this a right triangle?
I bet it is 37, 90, and 90-37 degrees.
To solve this problem, we can use the properties of right triangles and the relationships among their angles.
Let's label the triangle as ABC, where A is the point on the ground directly below the top of the building, B is the top of the building, and C is the initial point 200 yards away from the building.
First, we know that angle BAC is 90 degrees because the building forms a right angle with the ground.
Next, let's find angle ABC, the angle of elevation. Given that the angle of elevation from point C to the top of the building is 37 degrees, we have angle ABC = 90 degrees - angle BAC = 90 degrees - 37 degrees = 53 degrees.
Finally, to find angle ACB, we can use the fact that the sum of the angles in a triangle is 180 degrees. Therefore, angle ACB = 180 degrees - angle BAC - angle ABC = 180 degrees - 90 degrees - 53 degrees = 37 degrees.
Therefore, the measure of the angles of the triangle formed by the building, the ground, and the line of sight to the top of the building are:
Angle BAC = 90 degrees
Angle ABC = 53 degrees
Angle ACB = 37 degrees.
To find the measure of the angles of the triangle formed by the building, the ground, and the line of sight to the top of the building, we can start by drawing a diagram.
Let's label the triangle ABC, where A is the top of the building, B is the foot of the building, and C is the point on the ground where you are standing.
Given that the angle of elevation from point C to the top of the building is 37 degrees, we can label angle BAC as 37 degrees.
Now, since the sum of the angles in any triangle is 180 degrees, we can find the measure of the remaining angles.
Angle BCA is a right angle, as it is formed by a vertical line (the building) and a horizontal line (the ground). So, angle BCA is 90 degrees.
To find angle ABC, we can use the fact that the sum of the angles in a triangle is 180 degrees. So, angle ABC = 180 - (angle BAC + angle BCA).
= 180 - (37 + 90)
= 180 - 127
= 53 degrees.
Therefore, the measure of the angles in the triangle formed by the building, the ground, and the line of sight to the top of the building are:
angle BAC = 37 degrees
angle ABC = 53 degrees
angle BCA = 90 degrees