# Trigonometry

posted by .

If a stake is placed in the ground and is 20cm. high and casts a shadow 12.5 cm. long, what time is it? (The sun rises at 6 a.m. and is overhead at noon.)

• Trigonometry -

Major assumption ....
You must be at the equator , or between the two Cancers.

tanØ = 20/12.5 = 1.6
Ø = 57.99 or 58°

The assumption is that the time from 6:00 am to noon, or 6 hours , is proportional to the angle of the sun from 0° to 90°

t/6 = 58/90
t = 6(58/90) = 3.8666..
= 3 hrs and 52 minutes

the time is 9:52 am

## Similar Questions

1. ### PreCalc

The sun rises at 6 AM and is directly overhead at noon, estimate the time (hour and minutes) when a 34-foot tree will have a 14-foot shadow.
2. ### Trigonometry

Find the angle of elevation of the sun when a tower 100m high casts a shadow of 120 meter long?
3. ### trig

how high is a tree that casts a 30 ft shadow at the same time a 10 ft pole casts a shadow which is 10 ft long?
4. ### trig

as the sun rises it casts a long shadow over a boy who is leaning next to a tree. the tree is 35 feet tall and the sun's rays create an angle of depression of 70 degrees with the top of the tree. how long is the shadow
5. ### math

At a given time, the height of an object is directly proportional to the length of the shadow that is cast on the ground. A person 6 feet tall casts a shadow 1 foot long at noon. a) What is the length of the shadow cast by a flagpole …
6. ### calculus

If the sun rises at 6 AM and is directly overhead at 12 noon, estimate the time (hour and minutes) when a 34-foot tree will have a 24-foot shadow.
7. ### maths

16. A pole of length 10 m casts a shadow 2 m long on the ground. At the same time a tower casts a shadow of length 50 m on the ground, then find the height of the tower.
8. ### Math Geometry

The sun rises at 6am; At noon the sun is directly overhead. The height of a pole is 8m tall. What is the length of the shadow at 11am?
9. ### Trigonometry

A tree casts a shadow 38 m long. At the same time, the shadow cast by a 34 centimeter tall statue is 69 cm long. Find the height of the tree to the nearest tenth.
10. ### Spherical Trigonometry

*Approximate the angle of elevation of the sun if a box 5 meters tall casts a shadow 4 meters long on level ground. *As a weather ballon rises vertically its angle of elevation from a point P on the level ground 110km.from the point …

More Similar Questions