Planimetry - math word problems - page 163 of 187
Number of problems found: 3735
- A ship
A ship has been spotted by two lighthouses, A and B, as shown in the figure. What is the distance from the ship to Lighthouse A to the nearest tenth? Figure - the distance between lighthouses A and B is 40 nautical miles. From A is seen in view angle 57° - Observation tower
At the top of the hill, there is a 30-meter-high observation tower. We can see its heel and shelter from a certain point in the valley at elevation angles a=28°30" and b=30°40". How high is the top of the hill above the horizontal plane of the observation - Seats on carousel
There are 12 seats evenly distributed on the children's carousel in the shape of a circle. How long is the arm of the carousel (connecting the center of the carousel to the seat) if the distance between the two seats is 1.5 m? - Altitude angle
In complete winds-free weather, the balloon took off and remained standing exactly above the place from which it took off. It is 250 meters away from us. How high did the balloon fly when we saw it at an altitude angle of 25°? - The rescue helicopter
The rescue helicopter is above the landing site at a height of 180 m. The rescue operation site can be seen from here at a depth angle of 52°40'. How far will the helicopter land from the rescue site? - Right triangle trigonometrics
Calculate the size of the remaining sides and angles of a right triangle ABC if it is given: b = 10 cm; c = 20 cm; angle alpha = 60°, and the angle beta = 30° (use the Pythagorean theorem and functions sine, cosine, tangent, cotangent) - Position vector
The position vector of a point mass moving in a plane can be expressed in the established reference frame by the relation: r(t) = (1 + 5t + 2t² ; 3t + 1), where t is time in seconds and the vector coordinates are in meters. Calculate: a) What is the posit - Camera Blind Spot Length
The camera with a viewing angle of 120 ° was placed horizontally on the observatory at 30 m. What length d of the section at the tower's base can the camera not capture? - Steps
Find the height between the two floors if you know that the number of steps between the two floors is 18, the gradient is 30º, and the step length is 28.6 cm. Report the result in centimeters to the nearest centimeter. - In the desert
A man wondering in the desert walks 5.7 miles in the direction S 26° W. He then turns 90° and walks 9 miles in the direction N 49° W. At that time, how far is he from his starting point, and what is his bearing from his starting point? - ABS, ARG, CONJ, RECIPROCAL
Let z=-√2-√2i where i2 = -1. Find |z|, arg(z), z* (where * indicates the complex conjugate), and (1/z). Where appropriate, write your answers in the form a + i b, where both a and b are real numbers. Indicate the positions of z, z*, and (1/z) on an Argand - A rhombus 4
A rhombus has a side length of 10 cm. Find the angles at each vertex of the rhombus if the shorter diagonal measures 7 cm. Give your answers to the nearest degree and provide clear geometric reasoning at each step. - Distance Between Boats
An observer watches two boats at depth angles of 64° and 48° from the top of the hill, which is 75 m above the lake level. Determine the distance between the boats if both boats and the observer are in the same vertical plane. - Which
Which of the following numbers is the most accurate area of a regular decagon with side s = 2 cm? (A) 9.51 cm² (B) 20 cm² (C) 30.78 cm² (D) 31.84 cm² (E) 32.90 cm2 - 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 angles
Two endpoints distant 240 m are inclined at an angle of 18°15'. The top of the mountain can be seen at elevation angles of 43° and 51° from its. How high is the mountain? - Carousel for children
There are 5 seats evenly distributed on the children's carousel in the shape of a circle. What kind the arm of the carousel (connecting the center of the carousel to the seat) is long if the distance between with two seats is 1.2 m? - Embankment Width Calculation
An embankment 7.5 m high should be built on the horizontal plane. The width of the upper surface of the embankment is 2.9 m, and the slope is 35 °. What will be the lower width of the embankment? - Diamond angles
The diagonals in diamond KLMN are 10 cm and 6 cm long. Determine the angle size that the longer diagonal makes with the side of the diamond. - Component weight
The component is a regular decagon with a side of 2 cm. Its material weight of 1 m² of sheet metal is 24 kg. What is the weight of 200 components?
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