Goniometry and trigonometry - math word problems - page 19 of 28
Number of problems found: 559
- Tower's view
From the church tower's view at the height of 65 m, the top of the house can be seen at a depth angle of alpha = 45° and its bottom at a depth angle of beta = 58°. Calculate the height of the house and its distance from the church. - The tower
The observer sees the tower's base 96 meters high at a depth of 30 degrees and 10 minutes and the top of the tower at a depth of 20 degrees and 50 minutes. How high is the observer above the horizontal plane on which the tower stands? - Determine 18223
From the sine theorem, determine the ratio of the sides of a triangle whose angles are 30 °, 60 °, and 90 °. - Difference 6029
Between the resorts is 15km, and the climb is 13 per mille. What is the height difference?
- Decide 2
Decide whether points A[-2, -5], B[4, 3], and C[16, -1] lie on the same line - Rhombus
ABCD is a rhombus, ABD is an equilateral triangle, and AC is equal to 4. Find the area of the rhombus. - Climb
The road has climbing 1:27. How big is an angle correspond to this climbing? - Road
The angle of a straight road is approximately 12 degrees. Determine the percentage of this road. - Descent of road
The road sign informs us the gradient is 10.9%. Calculate the angle at which the average decreases.
- Calculate
Calculate the area of triangle ABC if given by alpha = 49°, beta = 31°, and the height on the c side is 9cm. - Traffic sign
There is a traffic sign for climbing on the road with an angle of 7%. Calculate at what angle the road rises (falls). - Cosine
Calculate the cosine of the smallest internal angle in a right-angled triangle with cathetus 3 and 8 and the hypotenuse 8.544. - Maximum area of rhombus
Calculate the interior angles at which the equilateral rhombus has a maximum area. - 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?
- River
From the observatory 11 m high and 24 m from the riverbank, river width appears in the visual angle φ = 13°. Calculate the width of the river. - Clouds
We see the cloud under an angle of 26°10' and the Sun at an angle of 29°15'. The shade of the cloud is 92 meters away from us. Approximately at what height is the cloud? - 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 in the direction of N 55° W. At that time, how far is he from his starting point? (Round your answer to two decimal places.) - Angle between vectors
Find the angle between the given vectors to the nearest tenth degree. u = (6, 22) and v = (10, -11) - Depth angles
At the top of the mountain stands a castle with a tower 30 meters high. We see the crossroad at a depth angle of 32°50' and the heel at 30°10' from the top of the tower. How high is the top of the mountain above the crossroad?
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