Given the value of the trigonometric ratio, find the value of b in the following diagrams. Round your answers to one decimal place if necessary.
\cos x = 0.75
\tan \theta = 0.4
\sin x = \dfrac{4}{5}
\tan \theta = \dfrac{2}{3}
Consider the following triangle:
Find an expression for \tan x.
If x = 39\degree and a = 10, solve for b, rounding your answer to one decimal place.
If x = 25 \degree and b = 7, solve for a, rounding to one decimal place.
Consider the given diagram:
Should the length of the side opposite the 32 \degree angle be greater than or less than 9 \text{ m}? Explain your answer.
Find the value of b in one decimal place.
Find the value of the pronumeral in the following triangles, correct to two decimal places:
The diagram shows a rectangle with a diagonal measuring f \text{ cm}:
Find the value of f, correct to two decimal places.
The diagram shows a rectangle with a side length measuring h \text{ mm}:
Find the value of h, correct to two decimal places.
The parallelogram shown has a side length measuring x \text{ cm}:
Find the value of x, to the nearest centimetre.
Consider the shape given:
Find the value of d, correct to one decimal place.
Find the value of f, correct to one decimal place.
AB is a tangent to a circle with centre O. OB is 24 \text{ cm} long and cuts the circle at C.
Find:
The length of the radius of the circle, r, to one decimal place.
The length of BC to the nearest centimetre.
A lighthouse is positioned at point A, and a boat is at point B. If d is the distance between the lighthouse and the boat, find d to two decimal places.
The distance from a point on the ground to the top of a tree measuring h \text{ m} is 23 \text{ m}. The angle between the line of sight and the ground is 29 \degree. Find the height of the tree to two decimal places.
In the following diagram, Neil's home is located at point A, and Neil is standing at point B.
If d is the distance between Neil and his home, find the value of d, correct to two decimal places.
The longer side of a rectangular garden measures 14 \text{ m}. A diagonal path makes an angle of 26\degree with the longer side of the garden. If the length of the shorter side of the garden is y \text{ m}, calculate y to two decimal places.
A 1.88 \text{ m} long ladder is leaning up against a wall at an angle of 38 \degree to the ground.
If d is the distance between the base of the wall and the base of the ladder, find d to two decimal places.
A ladder is leaning at an angle of 44 \degree against a 1.36 \text{ m} high wall.
Find the length of the ladder, to two decimal places.
A girl is flying a kite that is attached to the end of a 23.4 \text{ m} length of string. The angle between the string and the vertical is 21\degree. If the girl is holding the string 2.1 \text{ m} above the ground:
Find x, correct to two decimal places.
Hence, find the height h of the kite above the ground, correct to two decimal places.
Michael is facing due north and then turns around by exactly 130 \degree and walks for 67 \text{ m}.
How much further south is Michael compared to where he started? Round your answer to the nearest metre.
Laura needs to use a piece of paper in the shape of a regular pentagon to make an origami flower. The first step of the process is to fold along the dotted lines shown. The length of each fold line is 13.9 \text{ cm}.
What is the perpendicular height of the piece of paper? Round our answer to one decimal place.
What is the length of each side of the paper? Round your answer to one decimal place.
On Lerringdu Airlines, each passenger has a screen for entertainment attached to the chair in front of them. The screen has a height of 33.8 \text{ cm} and is able to tilt away from its frame by 20 \degree.
How far horizontally does the screen reach out from the seat in front when it is tilted away by 20 \degree? Round your answer correct to two decimal places.
Georgia is looking to buy a particular stand for her laptop. The picture of the stand in the catalogue shows the maximum angle of each part of the stand, along with the length of the stand's base.
Georgia wants to figure out the height of the stand when it is fully opened up.
Find the value of x, the length of the middle section of the stand. Round your answer to two decimal places.
Hence, find the value of h, the height of the stand. Round your answer to two decimal places.
