A diagram would surely help here. But imagine that you stand at spot A and someone finds that your distance from the base of the building is 42 feet. Call this point B.
Imagine a vertical line from that spot, straight up. Label the top of this line C.
The acute angle at A is 67 degrees. You want to find the height of the building, which would be the length of the "opposite side of triangle ABC."
The length of the "adjacent side of triangle ABC" would be 42 feet.
We don't know the length of the hypotenuse, altho' we could easilyl calculate it using the Pyth. Them.
We choose the tangent function to solve for the height of the building (which is the length of the opposite side.
height
By definition, tangent (67 degrees) = -------------------------------------
42 feet
Find tan 67. Multiply your result by 42 feet. This product is the height of the building.
Focus on triangles DFC and DFE:
- They are both right triangles because DF is perpendicular to EC
So, the two triangles are congruent. It follows that CF=FE, and in particular
And since x=3, the length of EF is
#2 is 35°C (just plug in 95 to the formula)
#3:
in the left column are:
(8x-(6+y))
(3/4)w+x^2
in the right column are:
y^2-0.5w
w/4+3(x+y)
to solve you just plug in to the formula
