Triangle practice problems - page 60 of 126
Number of problems found: 2520
- Ground speed
The plane flies south at an average speed of 190 km/h, and the wind blows from west to east at a speed of 20 m/s. How fast and in what direction (relative to the meridian) will the plane move relative to the ground? - A man 7
A man wandering in the desert walks 3.8 miles in the direction of S 44° W. He then turns and walks 2.2 miles toward N 55° W. At that time, how far is he from his starting point? (Round your answer to two decimal places.) - Reverse Pythagorean theorem
Given are the lengths of the sides of the triangles. Decide which one is rectangular: Δ ABC: 66 dm, 60 dm, 23 dm ... Δ DEF: 20 mm, 15 mm, 25 mm ... Δ GHI: 16 cm, 20 cm, 12 cm ... Δ JKL: 58 cm, 63 cm, 23 cm ... Δ MNO: 115 mm, - Angle of diagonals
Calculate the perimeter and area of a rectangle whose diagonal is 14 cm and whose diagonals form an angle of 130°. - An observer
An observer standing west of the tower sees its top at an altitude angle of 45 degrees. After moving 50 meters to the south, he sees its top at an altitude angle of 30 degrees. How tall is the tower? - Climb
The road sign that informs the climb is 10.3%—the car drives 10 km along this road. What is the height difference that the car went? - Perimeters
A rectangle has a perimeter of 16p centimeters. It had a width of 2p centimeters. Each side of an equilateral triangle is 1/2 the length of the rectangle. Find the total perimeter of the rectangle and the triangle if p=8. - Rectangle measurements
In the ABCD rectangle, the AB side is 16 cm long, and the AC diagonal is 20 cm long. Calculate the perimeter and area of the rectangle. - An azimuth
The patrol had started at a designated marching angle (an azimuth) of 13°. After 9 km, the azimuth's angle changed to 62°. The patrol went 10 km in this direction. Find the distance from where the patrol started. - Body collision momentum
A body with a mass of 4 kg hits an obstacle at a speed of 10 m/s. After the collision, the body continued to move at a speed of 6 m/s, while the direction of this speed was perpendicular to the direction of the speed before the collision. Find: a) change - Triangle
Calculate the area of the triangle ABC if b = c = 18 cm, R = 19 cm (R is the circumradius). - An equilateral
An equilateral triangle with a side of 10 m represents a wooden platform standing on a lawn. A goat is tied to a corner with a 15 m rope. What is the maximum amount of grazing area available to the goat? - Rectangle diagonal ratio
The aspect ratio of the rectangle and its diagonal is 9:12:15. Calculate the area of the rectangle if the length of the diagonal is 105 cm. - Circles
Three circles with radii 30 cm, 28 cm, and 37 cm are mutually tangent externally. What is the perimeter of the triangle whose vertices are the centres of the circles? - Right-angled triangle
The right-angled triangle XYZ is similar to the triangle ABC, which has a right angle at the vertex X. The following applies: side a = 9 cm, x=4 cm, x = v-4 (v = height of triangle ABC). Calculate the unknown side lengths of both triangles. - Airplane navigation
An airplane leaves an airport and flies west 120 miles and then 150 miles in the direction S 35.95°W. How far is the plane from the airport (round to the nearest mile)? - Rectangle
There is a rectangle with a length of 12 cm and a diagonal 8 cm longer than the width. Calculate the area of a rectangle. - Triangle similarity area
The area of a right-angled triangle KLM with a right angle at the vertex L is 60 mm square, and its hypotenuse k is 10 mm long. Triangles KLM and RST are similar. The similarity ratio is k=2.5. Calculate the area of triangle RST. - Area and two angles
Calculate the size of all sides and internal angles of a triangle ABC if it is given by area S = 501.9; and two interior angles α = 15°28' and β = 45°. - Right-angled triangle
Determine the area of a right triangle whose side lengths form successive members of an arithmetic progression, and the radius of the circle described by the triangle is 5 cm.
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