With respect to the given angle, what is the ratio of the opposite side to the hypotenuse?

It is the angle between the horizontal line from the observer and the line of sight to an object that is below the horizontal line.

It is the angle between the horizontal line from the observer and the line of sight to an object that is above the horizontal line.

Any of various instruments for measuring angles of elevation or inclination

Evaluate Sine 90⁰

Evaluate Cosine 90⁰

The expression 2( sin 30⁰ ) – tan 45⁰ is equal to

Triangle BCA is a right-angled at C. If c=23 and b = 17, find A

Triangle BCA is a right-angled at C. If c=23 and b = 17, find B

Triangle BCA is a right-angled at C. If c=23 and b = 17, find a

Triangle BCA is a right-angled at C if c=27 and A=58⁰, find B

Triangle BCA is a right-angled at C if c=27 and A=58⁰, find b

Triangle BCA is a right-angled at C if c=27 and A=58⁰, find a

A kite held by 125 m of string makes an angle of elevation with the ground of 45⁰. About how high is the kite above the ground?

From the top of the barn 7.62 m high, you can see a cat on the ground. The angle of depression of a cat is 40⁰. How many meters must the cat walk to reach the barn?

ABCD is a parallelogram. If AB is 8 cm ling, BC is 5 cm and their included angle measures 100⁰, how long is the diagonal AC?

In right triangle PQR, PR=13 cm, PQ =12 cm and QR=5 cm. What is cos R?

XYZ is an oblique triangle. If XY measures 20 cm, XZ measures 15 cm and angle Z measures 35⁰ then what is the measure of angle Y?

In right triangle ABC, BC =8cm and AC=17cm. Find the value of sin C.

PQRS is a rhombus with a side 5 cm long. If the measure of angle P is 140⁰, find the length of its longer diagonal.

Mr. De Guzman has a triangular-shaped backyard. Find the area of the backyard if two of its sides measures 8 m and 10 m, and the angle between these sides is 54⁰.

From an airplane at an altitude of 1500 m, the angle of depression to a rock on the ground measures 29⁰. Determine the distance from the plane to the rock.

From a point in the ground 7.62 m from the foot of the tree, the angle of elevation from the top of the tree is 32⁰. Determine the height of the tree to the nearest hundredths.

Two roads intersect at an angle of 100⁰. Chester’s mailbox is 8 m from the intersection. Dante’s mailbox is on the other road and is 12 m from the intersection. How far is Dante’s mailbox from that of Chester’s?

A man 1.5 m tall is on the top of the building. He observes car on the road 75⁰. If the building is 30 m high, how far is the car from the building?

A four meter ladder leans against the wall. If the foot of the ladder makes an angle of 80⁰ with the ground, how high up the wall does the ladder reached?

An airplane took off from an airport and travel a constant rate and the angle of elevation. When the airplane reached an altitude of 400 m, its horizontal distance from the airport was found to be 235 m. What was the angle when the airplane rose from the ground?

Jeo is flying a kite. He is holding the end of the string at the distance of 1.5 m above the ground, if the string is 20 m long and makes an angle of 40⁰ with the horizontal, how high is the kite above the ground?

A balloon is 50 m high. Its angle of elevation from observer is 45⁰ and from the observer B it is 30⁰. What is the maximum distance between the two observers? Express your answer to the nearest meter.

With the sun, a girl 1.4 m tall cast a 3.6 m shadow. Find the angle of elevation from the tip of the shadow to the sun. Express your answer to nearest degree.

You are walking on a straight level path toward a mountain. At one point the angle of elevation of the top of the mountain is 40⁰. As you walk 250 m closer, the angle of elevation is 45⁰. How high is the mountain? Express your answer to the nearest tenth of a meter.

Two points P and Q on the same side of a river are 12 m apart. A tree on the opposite side of the river is directly opposite a point P and Q. The lines of sight of a tree across the river make angles 78⁰ and 57⁰ respectively, with the line joining P and Q. Find the distance from point P and Q to the tree. Express your answer to the nearest meter.

. A surveyor sights two signs of the angle between two lines of the sight measures 55⁰. If the first and second signs are 70 m and 50 m away, respectively, from the surveyor, find the distance between the two signs. Express your answer to the nearest meter.

Two ships leave the same port at the same time. One ship sails on a course of 110⁰ at 32 mi/h. The other sails on a course of 230⁰ at 40 mi/h. Find the distance between them after 2 hours. Express your answer to the nearest mile.

The angle of elevation of the sun is 28⁰ and the shadow of the flagpole on horizontal ground is 29.5 ft. How tall is the flagpole?

Suppose a 50 feet high tree casts a shadow of length 60 feet, what is the angle of elevation from the end of the shadow to the top of the tree with respect to the ground?

How far from the door must a ramp begin in order to rise 3 feet with 8⁰ angle of elevation?

A tower is 15.24 m high. At a certain distance away from the tower, an observer determines that the angle of elevation to the top of it is 41. How far is the observer from the base of the tower?

At a point 42.3 feet from the base of a building, the angle of the top is 75⁰. How tall is the building?

An airplane is flying at a height of 4 kilometers above the ground. The distance along the ground from the airplane to the airport is 6 kilometers. What is the angle of depression from the airplane to the airport?

A hiker is 400 meters away from the base of the radio tower. The angle of elevation to the top of the tower is 46⁰. How high is the tower?

An observer in a lighthouse 48.8 m above the sea level saw two vessels moving directly towards the lighthouse. He observed that the angles of depression are 42⁰ and 35⁰. Find the distance between two vessels, assuming that they are coming from the same side of the tower.

A triangular field has sides 500 feet, 450 feet and 720 feet. Find the measure of the angle between the sides measuring 500 feet and 720 feet. Round off your answer to the nearest degree.