Goniometry and trigonometry - practice problems - page 2 of 32
Number of problems found: 626
- A tree 3
A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30° with it. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree. - Rhombus 36
Rhombus ABCD with side 8 cm long has diagonal BD 11.3 cm long. Find angle DAB. - A lighthouse
A lighthouse overlooks a bay, and it is 77 meters high. From the top, the lighthouse keeper can see a yacht southward at an angle of depression of 32 degrees and another boat eastward at an angle of 25 degrees. What is the distance between the boats? - Piece of a wire
A piece of wire is bent into the shape of a triangle. Two sides have lengths of 24 inches and 21 inches. The angle between these two sides is 55°. What is the length of the third side to the nearest hundredth of an inch? A: The length of the third side is - Cplx sixth power
Let z = 2 - sqrt(3i). Find z6 and express your answer in rectangular form. if z = 2 - 2sqrt(3 i) then r = |z| = sqrt(2 ^ 2 + (- 2sqrt(3)) ^ 2) = sqrt(16) = 4 and theta = tan -2√3/2=-π/3 - A triangle 7
A triangle lot has the dimensions a=15m, b=10m, and c=20m. What is the measure of the angle between the sides of b and c? - Conjugate coordinates
If the rectangular conjugate of the polar vector 12 angle 35 degrees is equal to x+yi, find the sum of x and y. - Cosine - legs
Using the law of cosines, find the measurement of leg b if the givens are β=20°, a=10, and c=15. - The apothem
The apothem of a regular hexagon is 5√3 inches. Find one of its sides and area. - A boy 5
A boy starts at A and walks 3km east to B. He then walks 4km north to C. Find the bearing of C from A. - Building shadow
When Sun's altitude 30° above the horizontal, then find the length of the shadow of a 50 m high of a building . - Angle and slope
Find the angle between the x-axis and the line joining the points (3, -1) and (4,-2) . - Vertical components
Find the horizontal and vertical components of the vector which has magnitude 750 as shown in the following figure. - Trigonometric fx
When an acute angle φ is in the standard position, its terminal side passes through point P (1,3). Find trigonometric functions of angle θ : sin φ, cos φ, tan φ, cotan φ. - Cotangent
If the angle α is acute, and cotan α = 1/3. Determine the value of sin α, cos α, and tan α. - Trigonometry
Is true equality? sin(x +13 π)= sin(x) - Observatories A,B
The target C is observed from two artillery observatories, A and B, 296 m apart. At the same time, angle BAC = 52°42" and angle ABC = 44°56". Calculate the distance of the target C from observatory A. - Substitution method
Solve a goniometric equation: sin4 θ - 1/cos² θ=cos² θ - 2 - Rectangular roof
Our house's roof is rectangular. When it rains, the water drains through the gutter. How much water flowed from our roof during a storm when we know that 12 liters of water fell on every 1 m² of surface? The roof width is 6m, the length is 9m, and the slo - 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 1.5m?
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