Use the inverse of tangent to solve for the approximate angle measure of vertex
C
, rounded to the nearest whole degree.
the sides are 9,15,12
the awsners to pick from are 37 degrees,59degrees,53degrees,39degrees
To find the angle measure of vertex C, we will use the Law of Cosines to first find angle A:
c^2 = a^2 + b^2 - 2ab * cos(C)
where c = 9 (side opposite angle C), a = 12 (side opposite angle A), b = 15 (side opposite angle B), and C = angle C.
Plugging in the values:
9^2 = 12^2 + 15^2 - 2(12)(15) * cos(C)
81 = 144 + 225 - 360 * cos(C)
81 = 369 - 360 * cos(C)
360 * cos(C) = 288
cos(C) = 288 / 360
cos(C) = 0.8
Now, we will use the inverse tangent function to find the angle measure of C:
C = arctan(0.8)
C ≈ 37 degrees
Therefore, the approximate angle measure of vertex C is 37 degrees. Choose the answer option 37 degrees.
Dedrea is making a bike ramp on the sidewalk in front of their house. They place a wood plank on top of blocks to form the ramp. The blocks are one foot in height, and the distance from the base of the blocks to where the wood plank touches the sidewalk is five feet. What is the approximate angle formed between the sidewalk and the base of the ramp?(1 point) the awnsers to pick from are 79degrees,11degrees,23degrees,45degrees
To find the angle formed between the sidewalk and the base of the ramp, we can use the tangent function.
Let x be the angle we want to find. The tangent of the angle x is equal to the opposite side (1 foot, height of the blocks) divided by the adjacent side (5 feet, distance from the base of the blocks to the sidewalk).
tan(x) = 1/5
Now, to find the angle x, we take the inverse tangent:
x = arctan(1/5)
x ≈ arctan(0.2)
x ≈ 11 degrees
Therefore, the approximate angle formed between the sidewalk and the base of the ramp is 11 degrees. Choose the answer option 11 degrees.
Right triangle
LMN
is drawn on paper. The right angle is located at vertex
L
with side length
MN
as the hypotenuse. The side length measurements are
LM=8 units
,
MN=10 units
, and
NL=6 units
. What is the approximate angle measure at vertex
N
?(1 point) the awnsers you can pick from are 39 degrees,53 degrees, 37 degrees,31 degrees
To find the approximate angle measure at vertex N, we can use the trigonometric ratios in a right triangle.
Given the side lengths:
LM = 8 units (side adjacent to angle N)
MN = 10 units (hypotenuse)
NL = 6 units (side opposite to angle N)
We can use the sine function since we are given the opposite and hypotenuse sides:
sin(N) = opposite/hypotenuse
sin(N) = 6/10
sin(N) = 0.6
Now, to find the angle measure at vertex N, we take the inverse sine function:
N = arcsin(0.6)
N ≈ 36.87 degrees
Therefore, the approximate angle measure at vertex N is 37 degrees. Choose the answer option 37 degrees.