Trigonometric Word Problems

A ladder is leaning against a wall. If the ladder is 10 meters long and makes an angle of 60 degrees with the ground, how high up the wall does the ladder reach?

• 10 meters

• 7.5 meters

• 5 * sqrt(3) meters

• 8 meters

In a right triangle, one acute angle measures 30 degrees. If the hypotenuse is 10 cm long, find the length of the side opposite the 30-degree angle.

• 7 cm

• 5 cm

• 3 cm

• 8 cm

An airplane is flying at an altitude of 5000 meters. If the angle of elevation from a ground observer to the airplane is 30 degrees, how far away is the airplane from the observer?

• 10 000 metres

• 6000 metres

• 4000 metres

• 7500 metres

In a right triangle, one acute angle measures 45 degrees. If the hypotenuse is 8 cm long, find the length of the other two sides.

• The length of the other two sides is 4 cm each.

• The length of the other two sides is 7.5 cm each.

• The length of the other two sides is 10 cm each.

• The length of the other two sides is approximately 5.66 cm each.

A person standing 20 meters away from a tree looks up at an angle of 30 degrees to the top of the tree. If the person is 1.5 meters tall, find the height of the tree.

• The height of the tree is approximately 15.5 meters.

• The height of the tree is approximately 20 meters.

• The height of the tree is approximately 11.54 meters.

• The height of the tree is approximately 13.04 meters.

A boat is 100 meters away from a lighthouse. If the angle of elevation from the boat to the top of the lighthouse is 45 degrees, how tall is the lighthouse?

• 50 meters

• 75 meters

• 125 meters

• 100 meters

A ramp is inclined at an angle of 20 degrees. If the ramp is 5 meters long, how high is the top of the ramp from the ground?

• 1.71 meters

• 4.2 meters

• 6.8 meters

• 2.5 meters

A person is flying a kite with a string of 50 meters. If the angle of elevation from the person to the kite is 70 degrees, how high is the kite above the ground?

• 50 meters

• 46.98 meters

• 46 meters

• 50.01 meters

A building casts a shadow of 30 meters when the angle of elevation of the sun is 40 degrees. Find the height of the building.

• 20.345 meters

• 28.765 meters

• 32.890 meters

• 25.173 meters

An airplane is flying at an altitude of 8000 meters. If the angle of elevation from a ground observer to the airplane is 45 degrees, how far away is the airplane from the observer?

• 11,313.71 meters

• 10,000 meters

• 9000 meters

• 7500 meters