Goniometry and trigonometry - practice problems - page 2 of 30
Number of problems found: 589
- 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?
- The apothem
The apothem of a regular hexagon is 5√3 inches. Find one of its sides and area. - 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. - 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. - Angle and slope
Find the angle between the x-axis and the line joining the points (3, -1) and (4,-2) . - Cosine - legs
Using the law of cosines, find the measurement of leg b if the givens are β=20°, a=10, and c=15.
- 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) - Sinus
Determine the smallest integer p for which the equation 4 sin x = p has no solution. - Modulus and argument
Find the mod z and argument z if z=i
- Substitution method
Solve a goniometric equation: sin4 θ - 1/cos² θ=cos² θ - 2 - Perpendicular 17423
According to the map, the scouts were supposed to proceed through the forest perpendicular to its straight edge, where the goal was 3 km away from the starting point. They already deviated from the correct direction by 5° at the start. How far from the ta - 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 - Entrepreneur 6309
Renting a 1m² advertising board costs €780 per month. A rectangular advertising board has a length of 3 m and its diagonal makes an angle of 34 degrees with the longer side. Calculate how much € an entrepreneur will pay for 4 months of renting a blackboar - Altitude angles
Cities A, B, and C lie in one elevation plane. C is 50 km east of B, and B is north of A. C is deviated by 50° from A. The plane flies around places A, B, and C at the same altitude. When the aircraft is flying around B, its altitude angle to A is 12°. Fi
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 observationDo you have homework that you need help solving? Ask a question, and we will try to solve it. Solving math problems.
