In ΔOPQ, the measure of ∠Q=90°, the measure of ∠P=54°, and OP = 68 feet. Find the length of PQ to the nearest foot.

PQ= 40 feet (nearest foot)

Step-by-step explanation:

Please see attached picture for full solution.

sin angle= opp/hyp

cos angle= adj/hyp

tan angle= opp/adj

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)