Planimetrics - math word problems - page 163 of 185
Number of problems found: 3687
- Parallelogram diagonal size
Given is the parallelogram KLMN, in which we know the side sizes/KL/ = a = 84.5 cm, /KN/ = 47.8 cm, and the angle size at the vertex K 56°40'. Calculate the size of the diagonals. - Colored area
How large is the area colored brown inside a square of side 6 cm if each of the four brown circular segments is from a circle with a radius of the length of the square's side? The length of the circular segments is equal to the length of the side of the s - Black diamond run
Taleah is skiing down a black diamond run. She begins skiing at the top of a ski trail whose elevation is about 8625 feet. The ski run ends toward the base of the mountain at 3800 feet. The horizontal distance between these two points is about 4775 feet. - Centre of the hypotenuse
The interior angles of the triangle ABC, alpha, beta, and gamma are in a ratio of 1:2:3. The longest side of the AB triangle is 30 cm long. Calculate the perimeter of the triangle CBS if S is the center of the side AB. - River bank distance
Adam (A) stands on one river bank, and Bedrich (B) stands on the other. To determine their distance, the base AC with a length of 136 m and the angles CAB with a size of 70°21' and ACB with a size of 43°44' were measured on one river bank. What is the dis - Tower distance angle
From the smaller observation tower, we see the top of the larger tower at an elevation angle of 23°, and the difference in their heights is 12 m. How far apart are the observation towers? - Tree
How tall is the tree observed at the visual angle 45°? If I stand 3 m from the tree, my eyes are two meters above the ground. - Binibini
Binibini owns a triangular residential lot bounded by two roads intersecting at 70°. The sides of the lot along the road are 62m and 43m, respectively. Find the length of the fence needed to enclose the lot. (express answers to the nearest hundredths) - Circle line probability
A rectangular grid consists of two mutually perpendicular systems of parallel lines with a distance of 2. We throw a circle with a diameter of 1 on this plane. Calculate the probability that this circle: a) overlaps one of the straight lines; b) do any of - Triangle tangent area
In the triangle ABC, b=5 cm, c=6 cm, /BAC/ = 80° are given. Calculate the sizes of the other sides and angles, and further determine the sizes of the tangent tc and the area of the triangle. - Trigonometric equation solving
Solve the trigonometric equation: cos (x-52°) = 1 - A construction
A construction worker is trying to find the height of a skyrise building. He is standing some distance away from the base with an elevation angle of 65 degrees. The worker moves 50 feet closer and measures the angle of elevation to be 75 degrees. Find the - Parallelogram diagonals
Find the area of a parallelogram if the diagonals u1 = 15 cm and u2 = 12 cm and the angle formed by them is 30 degrees. - Viewing angle
The observer sees a straight fence 60 m long at a viewing angle of 30°. It is 102 m away from one end of the enclosure. How far is the observer from the other end of the enclosure? - Calculate triangle
In the triangle, ABC, calculate the sizes of all heights, angles, perimeters, and areas if given a=40cm, b=57cm, and c=59cm. - Parallelogram diagonal construction Construct a parallelogram ABCD if a=5 cm, height to side a is 5 cm, and angle ASB = 120 degrees. S is the intersection of the diagonals.
- Elevation angle
An airliner currently flying over a location 2,400 m away from the observer's location is seen at an elevation angle of 26° 20'. At what height does the plane fly? - Sailboat
The 20 m long sailboat has an 8 m high mast in the middle of the deck. The top of the mast is fixed to the bow and stern with a steel cable. Determine how much cable is needed to secure the mast and what angle the cable will make with the ship's deck. - Rectangular
Rectangular triangle KLM with right angle at vertex L, angle beta at vertex K, and angle alpha at vertex M. Angle at vertex M = 65°, side l = 17.5 cm. Use Pythagorean theorems and trigonometric functions to calculate the lengths of all sides and the angle - A trapezoid
A trapezoid with a base length of a = 36.6 cm, with angles α = 60°, β = 48°, and the height of the trapezoid is 20 cm. Calculate the lengths of the other sides of the trapezoid.
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