Goniometry and trigonometry - practice problems - page 5 of 32
Number of problems found: 634
- Maggie
Maggie observes a car and a tree from a window. The angle of depression of the car is 45 degrees, and that of the tree is 30 degrees. If the distance between the vehicle and the tree is 100 m, find Maggie's distance from the tree. - Right angled triangle 3
Side b = 1.5, hypotenuse angle A = 70 degrees, Angle B = 20 degrees. Find the length of its unknown sides. - The mast
A 40 m high mast is secured in half by eight ropes 25 m long. The ends of the ropes are equidistant from each other. Calculate this distance. - How far
From the top of a lighthouse 145 ft above sea level, the angle of depression of a boat is 29°. How far is the boat from the lighthouse? - View angle
From a tower 20 m high and 20 m away from a river, the width of the river appears to span an angle of 15°. How wide is the river at this location? - Mirror
The dimensions of a mirror are 750 mm × 700 mm, and the mirror is to be tilted 8° away from the wall. How many centimetres must the bottom of the mirror protrude from the wall? - In a right-angled 17
In right triangle DEF with hypotenuse f = 12 cm, the interior angle at vertex D is 60°. What is the length of side e? - Ropeway angle length
The ropeway climbs at an angle of 22°30'. Calculate its length if the height difference between the lower and upper station is 560 m. Sketch a picture - Rhombus diagonals
In the rhombus ABCD, the sizes of the diagonals e = 24 cm and f = 10 cm are given. Calculate the side length of the diamond and the size of the angles, and then calculate the area of the diamond. - Depth angle
From a cliff of 150 meters high, we can see the ship at a depth angle of 9° at sea. How far is the ship from the cliff? - Rhombus area
Calculate the area and height of the rhombic cover plate to which the following applies: d (BC) = 60 cm, angle BAD = 45 °, angle ADB = 90 °. - Rectangle
Calculate the length of the side HM and diagonal EM of rectangle EHMQ when given: |QM| = 29 cm and angle ∠ EHQ = 36 degrees. - Cable car
A cable car rises at an angle of 44° and connects the upper and lower stations with an altitude difference of 1089 m. How long is the continuous (endless) tow rope? - Triangle SAA
A triangle has one side of length 23 m and two interior angles of 60°. Calculate its perimeter and area. - Tower elevation angles
Find the height of the tower when the geodetic measured two angles of elevation α=34° 30'' and β=41°. The distance between places AB is 14 meters. - Wall and ladder
A ladder leans against a wall, reaching a height of 6.5 m. How long is the ladder if it makes an angle of 60° with the horizontal floor? - Triangle 75
Triangle ABC has angle C bisected and intersected AB at D. Angle A measures 20 degrees, and angle B measures 40 degrees. The question is to determine AB-AC if length AD=1. - The airplane
The airplane sights a runway at an angle of depression of 23°. It is flying at an altitude of 3 kilometers above the ground. What is the horizontal distance of the airplane from the airport? - 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? - An isosceles trapezoid
An isosceles trapezoid has base angles of 50° each, and its bases are 20 cm and 30 cm. Compute its area.
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