Goniometry and trigonometry - practice problems - page 5 of 32
Number of problems found: 634
- 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. - Parallelogram - two sides
The parallelogram has the sides a = 25.3 b = 13.8, and the angle closed by the sides is a = 72°. Calculate the area of the parallelogram.
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