# Pre-Calc

posted by .

Both Derek and Sam are 5ft 10in tall. Derek looks at a 10ft basketball goal with an angle of elevation of 29 degrees, and Sam looks at the goal with an angle of elevation of 43 degrees. If Sam is directly in front of derek, how far apart are the boys standing?

• Pre-Calc -

Draw a side view of the situation, then the basket is 50 inches above the height of the the eyes of the two boys.
distance of derek to point below the basketball is x
of Sam to a point below the basketball is y

tan29 = 50/x ---> x = 50/tan29
tan 43 = 50/y --->y = 50/tan43

distance between the boys = x-y
= 50/tan29- 50/tan43
= 36.583 inches
= or 3.05 ft

## Similar Questions

1. ### physics

Derek the drunk driver drives his car off the road, onto a gravel strip next to the road. Derek does not have anti-lock brakes, so his wheels lock when he enters the gravel area, and the car slides to a halt. Derek's car is traveling …
2. ### Pre-Calculus

1.The angle of elevation to top of a building from a point on the ground 20degrees and the angle of elevation from a point to 25 feet farther away is 12degrees. Find the height of the building. 2.From a point on the ground, the angle …
3. ### Math

Derek wants to determine the height of the top of the backboard on the basketball goal at the playground. He places a standard 12-inch ruler next to the goal post and measures the shadow of the ruler and the backboard. If the ruler …
4. ### Maths

On Saturday Derek picked pears from 32 trees. His picked average of 17 pears per tree. Sunday he picked more pears averaging 12 pears per tree. Over the whole weekend he picked an average of 14 pears per tree. How many trees did Derek …
5. ### Math

1. A rangers tower is located 44m from a tall tree. From the top of the tower, the angle of elevation to the top of the tree is 28 degrees and the angle of depression to the base is 36 degrees. How tall is the tree?
6. ### Math, Analytic Geometry

Derek wants to determine the height of the top of the backboard on the basketball goal at the playground. He places a standard 12-inch ruler next to the goal post and measures the shadow of the ruler and the backboard. If the ruler …
7. ### math

Derek ran 3/8 of a race he had to stop for a break.If the race is 6 miles long,did Derek run more than,less than,or equal to 6 miles before he took a break?
8. ### Trigonometry

John stands on top of a little lighthouse looking out at a nearby tall lighthouse that is 200 feet away. He looks at the top of the tall lighthouse with a 3 degree angle of elevation, but looks at the bottom of the tall lighthouse …
9. ### math

A used guitar is on sale for \$280. Derek offers the seller 3/4 of the advertised price. How much does Derek offer for the guitar?