For △abc, which side is opposite angle b?

side ac

side ab

side bc

angle d in △edf is a right angle.

what is the value of tan f ?

4/3

3/4

3/5

4/5

what is the trigonometric ratio for sin z ?
enter your answer, as a simplified fraction, in the boxes.

what is the trigonometric ratio for cosd ?
enter your answer, as a simplified fraction, in the boxes.

tessa has leaned a ladder against the side of her house. the ladder forms a 63˚ angle with the ground and rests against the house at a spot that is 8 meters high.

which length is the best approximation for the distance along the ground from the bottom of the ladder to the wall?
2 m
3 m
4 m
5 m

Problem 1

side AC



Explanation:

Side AC is opposite angle B because it is the furthest you can get on the triangle to be away from point B. This segment is a leg of the right triangle. Note how the letter B is not anywhere to be found in AC.


Problem 2

4/3



Explanation:

angle D is the right angle, the side across from this right angle is the hypotenuse EF

with reference angle F, we have
opposite = ED = 4
adjacent = DF = 3

tan(angle) = opposite/adjacent
tan(F) = ED/DF
tan(F) = 4/3


Problem 3

3/5



Explanation:

Use the Pythagorean Theorem to find the missing side XY
a^2 + b^2 = c^2
(XY)^2 + (YZ)^2 = (XZ)^2
(XY)^2 + (32)^2 = (40)^2
(XY)^2 + 1024 = 1600
(XY)^2 + 1024-1024 = 1600-1024
(XY)^2 = 576
sqrt[ (XY)^2 ] = sqrt[ 576 ]
XY = 24

Use that value to find the trig ratio we need

sin(angle) = (opposite)/(hypotenuse)
sin(Z) = (XY)/(XZ)
sin(Z) = (24)/(40)
sin(Z) = (8*3)/(8*5)
sin(Z) = 3/5


Problem 4

7/25



Explanation:

cos(angle) = adjacent/hypotenuse
cos(D) = (ED)/(DF)
cos(D) = (21)/(75)
cos(D) = (7*3)/(25*3)
cos(D) = 7/25


Problem 5

4 meters



Explanation:

We want to find the horizontal distance from the ground to the foot of the ladder. Call this x for now. 

This x is the adjacent leg, since it is touching the 63 degree angle. The opposite side is 8 meters

opposite = 8
adjacent = x

Use the tangent function to solve for x

tan(angle) = opposite/adjacent
tan(63) = 8/x
x*tan(63) = x*(8/x)
x*tan(63) = 8
x*tan(63)/tan(63) = 8/tan(63)
x = 4.07620359595543
Rounding to the nearest whole number, we get 4 meters.

Dis the correct answer