# The tower

The observer sees the tower's base 96 meters high at a depth of 30 degrees and 10 minutes and the top of the tower at a depth of 20 degrees and 50 minutes. How high is the observer above the horizontal plane on which the tower stands?

### Correct answer:

Tips for related online calculators

Check out our ratio calculator.

Do you have a system of equations and looking for calculator system of linear equations?

See also our right triangle calculator.

Most natural application of trigonometry and trigonometric functions is a calculation of the triangles. Common and less common calculations of different types of triangles offers our triangle calculator. Word trigonometry comes from Greek and literally means triangle calculation.

Do you have a system of equations and looking for calculator system of linear equations?

See also our right triangle calculator.

Most natural application of trigonometry and trigonometric functions is a calculation of the triangles. Common and less common calculations of different types of triangles offers our triangle calculator. Word trigonometry comes from Greek and literally means triangle calculation.

#### You need to know the following knowledge to solve this word math problem:

**algebra**- system of equations
- expression of a variable from the formula
**planimetrics**- right triangle
**basic functions**- ratio
**goniometry and trigonometry**- tangent

#### Units of physical quantities:

#### Grade of the word problem:

We encourage you to watch this tutorial video on this math problem: video1

## Related math problems and questions:

- Depth angles

At the top of the mountain stands a castle with a tower 30 meters high. We see the crossroad at a depth angle of 32°50' and the heel at 30°10' from the top of the tower. How high is the top of the mountain above the crossroad? - An observer

An observer standing west of the tower sees its top at an altitude angle of 45 degrees. After moving 50 meters to the south, he sees its top at an altitude angle of 30 degrees. How tall is the tower? - Calculate 43331

From the lookout tower, 70 meters high, we see a man at a depth angle of 15 degrees. Calculate how far one stands from the base of the lookout tower. Draw and calculate. - Determine 8202

An observer watches two boats at depth angles of 64° and 48° from the top of the hill, which is 75 m above the lake level. Determine the distance between the boats if both boats and the observer are in the same vertical plane. - Mirror

How far must Paul place a mirror to see the top of the tower 12 m high? The height of Paul's eyes above the horizontal plane is 160 cm, and Paul is from the tower distance of 20 m. - An angle of depression

The lighthouse sees a ship at an angle of depression of 25°. The observer from the lighthouse is 82 m above sea level. How far is the ship from the top of the lighthouse? - A radio antenna

Avanti is trying to find the height of a radio antenna on the roof of a local building. She stands at a horizontal distance of 21 meters from the building. The angle of elevation from her eyes to the roof (point A) is 42°, and the angle of elevation from - TV tower

Calculate the height of the television tower if an observer standing 430 m from the base of the tower sees the peak at an altitude angle of 23°. - Tower's view

From the church tower's view at the height of 65 m, the top of the house can be seen at a depth angle of alpha = 45° and its bottom at a depth angle of beta = 58°. Calculate the height of the house and its distance from the church. - Hot air balloon

The center of the balloon is at an altitude of 600 m above the ground (AGL). The observer on earth sees the center of the balloon at an elevation angle of 38°20'. The balloon is seen from the perspective of an angle of 1°16'. Calculate the diameter of the - The farmer

The farmer sees the back fence of the land, which is 50 m long at a viewing angle of 30 degrees. It is 92 m away from one end of the fence. How far is it from the other end of the fence? - Elevation 80869

We can see the top of the tower standing on a plane from a certain point A at an elevation angle of 39° 25''. If we come towards its foot 50m closer to place B, we can see the top of the tower from it at an elevation angle of 56° 42''. How tall is the tow - Top-open tank

The top-open tank has the shape of a truncated rotating cone, which stands on a smaller base. The tank's volume is 465 m^{3}, and the radii of the bases are 4 m and 3 m. Find the depth of the tank. - Broken tree

The tree was 35 meters high. The tree broke at the height of 10 m above the ground. Top, but does not fall off. It is refuted on the ground. How far from the base of the tree lay its peak? - The Eiffel Tower

The top of the Eiffel Tower is seen from a distance of 600 meters at an angle of 30 degrees. Find the tower height. - Standing 22821

The heating plant sees the observer standing 26 m from the bottom of the chimney and sees the top at an angle of 67 °. How high is the chimney of the heating plant? - Reflector

The circular reflector throws a light cone with a vertex angle 49° and is on 33 m height tower. The axis of the light beam has the axis of the tower angle 30°. What is the maximum length of the illuminated horizontal plane?