In each right triangle ABC, find B. The right angle is at C.
1. a= 11.7 m, b= 14.9 m
2. The angle of depression from the top of a 64-ft-tall tower to a deer is 47 degrees 16 minutes. Find the distance from the deer to the bottom of the tower.
B=arctan b/a check that with a sketch.
2. 64/distance=tanTHeta
solve for distance.
To find angle B in each right triangle, we can use the trigonometric function, Tangent.
1. For the first right triangle with side lengths a = 11.7 m and b = 14.9 m, we can use the formula for the Tangent function:
Tangent(B) = a / b
Substituting the given values, we get:
Tangent(B) = 11.7 m / 14.9 m
Using a scientific calculator, find the inverse tangent (also called arctan or Tan^(-1)) of both sides to solve for B:
B = Tan^(-1)(11.7 m / 14.9 m)
Calculate this expression using the inverse tangent function. Be sure to set your calculator to the appropriate angle mode (degrees or radians) to match the given units.
2. For the second right triangle with the angle of depression given as 47 degrees 16 minutes and the length of the tower as 64 ft, we can use the Tangent function again:
Tangent(B) = Opposite / Adjacent
In this case, the opposite side is the height of the tower, and the adjacent side is the distance from the deer to the bottom of the tower.
We need to convert the angle from degrees and minutes to decimal degrees. To do this, divide the minutes value by 60 and add it to the degrees value.
Angle B = 47 + (16/60) degrees
Substituting the given values, we get:
Tangent(B) = 64 ft / distance from deer to bottom of tower
Rearranging the equation to solve for the distance from the deer to the bottom of the tower:
distance from deer to bottom of tower = 64 ft / Tangent(B)
Calculate the tangent of B, and then substitute it into the equation to find the distance from the deer to the bottom of the tower.