Notice the picture below
so.... the angle of depression, is above in dashed lines.... however, the angle of depression, is identical to the angle of elevation from the water, since, both angles are "alternate interior" angles
now, using the 45-45-90 rule, then we know the swimmer is 90 feet from the lighthouse, then just use the tangent ratio to get "x"
The steps below are presented in order to arrive to the value of k of the given equation.
First, multiply both sides of the equation by the variable k since the left-hand side of the equation has it in the denominator. This will be,
(k + 12/ k)(k) = 8(k)
Then, we simplify,
k + 12 = 8k
We then, subtract 8k to both sides of the equation,
k - 8k + 12 = 8k - 8k
Simplifying,
-7k + 12 = 0
Then, subtract 12 from both sides of the equation and divide both sides by -7. This will us the final answer of,
k = 12/7
Answer:
8 ft, 15 ft, 17 ft
Step-by-step explanation:
Let x feet be the length of the side along the building. If the hypotenuse is 9 feet longer than the side along the building, then the length of the hypotenuse is x+9 feet. If the third side is 7 feet longer than the side along the building, then the length of the third side is x+7 feet.
This triangle is right triangle. By the Pythagorean theorem,
The length of the side cannot be negative, thus x=8 ft. Then x+7=15 ft, x+9=17 ft.
We take interest+interest+interest to equal interest
0.041=4.1%(25000) the amount invested+0.056=interest they want=0.048 the total amount wanting to earn 4.8% and x is the added money to invest.
0.041(25000)+0.056x=0.048(25000+x)
1025+0.056x=1200+0.048x
subtract the 0.048 from both sides
1025+0.008x=1200+x
Subtract the 1025 from both sides
1025-1025+0.008=1200-1025+x
0.008x=175+x
Now divide 175 by 0.008
x=21,875
