16.01 Trigonometric ratios
For the following triangles, name the hypotenuse:
Consider the following triangle:
State the opposite side to angle \theta.
State the adjacent side to angle \theta.
State the opposite side to angle \alpha.
State the adjacent side to angle \alpha.
State the angle that is opposite the hypotenuse.
With reference the angle \theta, find the value of these ratios for each of the following triangles:
\dfrac{\text{Opposite }}{\text{Adjacent }}
\dfrac{\text{Opposite }}{\text{Hypotenuse }}
\dfrac{\text{Adjacent }}{\text{Hypotenuse }}
Write down the indicated ratios for the following triangles:
\tan \theta
\sin \alpha
\sin \theta
\tan \alpha
\cos \theta
\cos \alpha
\tan \theta
\sin \alpha
\cos \theta
\tan \alpha
Consider the following triangle:
Find the value of x.
Find the value of \sin \theta.
Find the value of \cos \theta.
Consider the following triangle:
Find the value of x.
Hence, find the value of \tan \theta.
For the following triangle, if \tan \theta = \dfrac{2}{3}, find the value of b.
For the following triangle, if \tan \theta = \dfrac{4}{3}, find the value of d.
For the following triangle, if \tan \theta = 0.4, find the value of b.
Round your answer correct to one decimal place.
Find the value of the pronumeral in the following triangles, correct to two decimal places:
Given the following triangle, calculate the exact value of \tan \theta.
For each of the following triangles, find the value of x to the nearest degree:
An isosceles triangle has equal side lengths of 10 \text{ cm} and a base of 8 \text{ cm} as shown.
Calculate the size of angle A to one decimal place.
Find the value of \tan \theta for the following triangle:
Find the value of the pronumeral(s) in the following diagrams, correct to the nearest whole number:
If d is the distance between the base of the wall and the base of the ladder, find the value of 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 ladder measuring 2.36 \text{ m} in length is leaning against a wall.
If the angle the ladder makes with the ground is y \degree, find the value of y 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. 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.
In the diagram, a string of lights joins the top of the tree to a point on the ground 23.9 \text{ m} away. If the angle that the string of lights makes with the ground is \theta \degree, find \theta to two decimal places.
A ladder measuring 1.65 \text{ m} in length is leaning against a wall. If the angle the ladder makes with the wall is y \degree, find y to two decimal places.
Find the value of \tan \theta in the following trapezium:
A sand pile has an angle of 40 \degree and is 10.6 \text{ m} wide.
Find the height of the sand pile, h, to one decimal place.
