Right triangle word problems worksheet with answers

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Exercise 1

The known data for a right triangle ABC is

and

. Solve the triangle.

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Exercise 2

The known data for a right triangle ABC is

and

. Solve the triangle.

Exercise 3

The known data for a right triangle ABC is

and

. Solve the triangle.

Exercise 4

The known data for a right triangle ABC is

and

. Solve the triangle.

Exercise 5

A tree

tall casts a shadow

long. Find the angle of elevation of the sun at that time.

Exercise 6

An airship is flying at an altitude of

when it spots a village in the distance with a depression angle of

. How far is the village from where the plane is flying over?

Exercise 7

Find the radius of a circle knowing that a chord of

has a corresponding arc of

Exercise 8

Calculate the area of a triangular field, knowing that two of its sides measure

and

and between them is an angle of

Exercise 9

Calculate the height of a tree, knowing that from a point on the ground the top of the tree can be seen at an angle of

and from 10 m closer the top can be seen at an angle of

Exercise 10

The length of the side of a regular octagon is

. Find the radii of the inscribed and circumscribed circles.

Exercise 11

Calculate the length of the side and the apothem of a regular octagon inscribed in a circle with a radius of

centimeters.

Exercise 12

Three towns A, B, and C are connected by roads that form a triangle. The distance from A to C is

and from B to C,

. The angle between these roads is

. How far are towns A and B from each other?

Solution of exercise 1

The known data for a right triangle ABC is

and

. Solve the triangle.

Solution of exercise 2

The known data for a right triangle ABC is

and

. Solve the triangle.

Solution of exercise 3

The known data for a right triangle ABC is

and

. Solve the triangle.

Solution of exercise 4

The known data for a right triangle ABC is

and

. Solve the triangle.

Solution of exercise 5

A tree

tall casts a shadow

long. Find the angle of elevation of the sun at that time.

Solution of exercise 6

An airship is flying at an altitude of

when it spots a village in the distance with a depression angle of

. How far is the village from where the plane is flying over?

Solution of exercise 7

Find the radius of a circle knowing that a chord of

has a corresponding arc of

Solution of exercise 8

Calculate the area of a triangular field, knowing that two of its sides measure

and

and between them is an angle of

Solution of exercise 9

Calculate the height of a tree, knowing that from a point on the ground the top of the tree can be seen at an angle of

and from 10 m closer the top can be seen at an angle of

equation 1

equation 2

Putting the value of x in equation 1:

Solution of exercise 10

The length of the side of a regular octagon is

. Find the radii of the inscribed and circumscribed circles.

Radius of the inscribed circle.

Radius of the circumscribed circle.

Solution of exercise 11

Calculate the length of the side and the apothem of a regular octagon inscribed in a circle with a radius of

centimeters.

Solution of exercise 12

Three towns A, B, and C are connected by roads that form a triangle. The distance from A to C is

and from B to C,

. The angle between these roads is

. How far are towns A and B from each other?

How do you do right triangle word problems on the SAT?

Right triangle word problems on the SAT ask us to apply the properties of right triangles to calculate side lengths and angle measures. Use the Pythagorean theorem and recognize Pythagorean triples Recognize special right triangles and use them to find side lengths and angle measures

How to solve a problem involving two right triangles using trigonometry?

To solve a problem involving two right triangles using trigonometry, draw and label a diagram showing the given information, and the length or angle measure to be found identify the two triangles that can be used to solve the problem, and plan how to use each triangle solve the problem and show each step in your solution

What is a word problem with trigonometry?

Trigonometry Word Problems The Primary Trigonometric Ratios – Word Problems A. Determining the measures of the sides and angles of right triangles using the primary ratios When we want to measure the height of an “inaccessible” object like a tree, pole, building, or cliff, we can utilize the concepts of trigonometry.

How do you find the unknown side of a triangle?

SOLVING FOR AN UNKNOWN SIDE OR ANGLE Where Do I Begin…Where Does It End? 1. Sketch the triangle, if one has not been provided for you. 2. Label the given angle(s) and side(s). Include the variable for the unknown side or angle, where needed. 3. “Looking” from the given angle, label the opposite side, adjacent side, and hypotenuse. 4.

Why are the skills in solving word problems involving right triangles important in real life?

Finding height or length In architecture, the experts solve right triangle problems to find the required height or length of any structure. This calculation is needed to assure compliance with the building plan.

What is the formula for angle of depression?

The angle of depression may be found by using this formula: tan y = opposite/adjacent. The opposite side in this case is usually the height of the observer or height in terms of location, for example, the height of a plane in the air. The adjacent is usually the horizontal distance between the object and the observer.