Need help with a few Trig problems.?

Question

1. Two cars reach a fork in the road at 9.00 AM. Car 1 takes due north road and drives at 88 mph. Car 2 drives north-east at 40 MPh. How far apart are the cars at 11.15am? At what time are the cars 100 Miles apart?

2. A family is driving towards a mountain. They stop to look up at the summit, with an angle of elevation of 20 degrees. After driving for another 5 miles towards the mountain, the angle of elevation is 42 degrees. How high is the mountain?

3. A baseball diamond has four bases, forming a square, that are 90 feet apart. The pitcher's mound is 60.5 feet from HOme plate, on the diagonal line separating home plate and second base. What is the distance from the pitchers mound to each of the other three bases.

Thanks a bunch

Answer 1

1) dist by car one is 100 m. distance by car 2 is 50 miles.

plane right angled triangle. course of car 2 is 045 ie the angle is 45.

so the third angle will be also 45.

so the distance apart will be 50 miles.

they will be 100 miles apart at 1230.

2) Tan 20 = height / distance

so 0.364 x dist = height.

after travelling 5 miles

Tan 42 = height / new distance.

0.9 x new distance = height.

height will be same

so

0.364 x distance = 0.9 x new distance.

but new distance = old distance - 5

0.364 x old distance = 0.9 (old distance -5)

solve

distance is 9.328 miles ( old)

new will be 4.328 miles.

use the value in the first equation to get height.

0.364 x 9.328 = height

base ball no clue because i dont know how it looks like and so cant help u.

though if the bases form a square of l = 90 then diagonal will be 127.28 feet.

pitcher is 60.5 from one base so from other base will be

127.28 - 60.5.

Answer 2

1- the time they drove is 2.25 hrs, car went north was at a distance of= 88x2.25= 198miles, the second was at 40x2.25= 90 miles, the angle between the cars is 45 degrees,then the distance between the two cars was 148.5 miles after 2.25 hrs, then after 1.5hrs they will be 100 miles apart.

2-assume the mountain height is " h " and the distance from the mountain at the angel of 42 is " x ", then

tan 42 = h/x =0.9 ,then h = 0.9x

tan 20 = h/(5+x) , then h = 0.36(5+x)=0.9x

solving the two equations gives x = 3.3 miles and h = 0.9x3.3= 3 miles the mountain height.

3- I don't understand baseball game therefore I can not imagine the base distribution, if you can draw it then i can solve this question.

good luck