Consider the following right-angled triangle:
Identify:
Consider the following right-angled triangle:
Which angle is opposite the hypotenuse?
Which side is opposite \angle B?
Which side is adjacent \angle C?
During a particular time of the day, a tree casts a shadow of length 24\text{ m}. The height of the tree is estimated to be 7\text{ m}.
In the given triangle, state whether the height of the tree or its shadow is:
The opposite side to the angle \theta.
The adjacent side to the angle \theta.
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 }}
Consider the given triangle:
For \angle ACB, find the value of the ratio \\ \dfrac{\text{opposite}}{\text{hypotenuse}}.
For \angle CAB, find the value of the ratio \\ \dfrac{\text{adjacent}}{\text{hypotenuse}}.
Consider the given triangle:
For \angle ACB, find the value of the ratio \\ \dfrac{\text{adjacent}}{\text{hypotenuse}}.
For \angle CAB, find the value of the ratio \\ \dfrac{\text{opposite}}{\text{hypotenuse}}.
Consider the following diagram:
With regards to the angle \theta, find the value of the following ratios:
Consider the following diagram:
Find the following ratio of sides, with respect to \theta:
\dfrac{\text{opposite}}{\text{adjacent}}
\dfrac{\text{adjacent}}{\text{hypotenuse}}
\dfrac{\text{opposite}}{\text{hypotenuse}}
Consider the diagram below:
Using the triangle created by the building, find the value of the fraction \dfrac{\text{opposite}}{\text{adjacent}} using the opposite side and adjacent adjacent side of \angle TAB.
The tree has a height of 21 metres. For the smaller triangle created by the tree, find the value of the fraction \dfrac{\text{opposite}}{\text{adjacent}} using the opposite side and adjacent adjacent side of \angle HAC.
Are the ratios from (a) and (b) equal?
Using the triangle created by the tree, find the value of the fraction \dfrac{\text{adjacent}}{\text{hypotenuse}} using the adjacent side and hypotenuse for \angle HAC.
Using the triangle created by the building, find the value of the fraction \dfrac{\text{opposite}}{\text{hypotenuse}} using the opposite side and hypotenuse for \angle TAB.
Are the ratios from (d) and (e) equal?
Write down the following ratios for the given triangle:
For the following triangles, determine \cos \theta:
Evaluate \sin \theta in the following triangles:
Find the value of \tan \theta in the following triangles:
Which trigonometric ratio relates the given sides and reference angle in the following triangles?
For each of the following triangles:
Find the value of x.
Find the value of \sin \theta.
Find the value of \cos \theta.
For each of the following triangles:
Find the value of the missing side.
Find the value of \tan \theta.
In the following triangle \sin \theta = \dfrac{4}{5}:
Which angle is represented by \theta?
Find the value of \cos \theta.
Find the value of \tan \theta.
In the following triangle \tan \theta = \dfrac{15}{8}.
Which angle is represented by \theta?
Find \cos \theta.
Find \sin \theta.
Consider the following triangle:
Find the value of \sin \theta.
Find the value of \cos \theta.
Find the value of \dfrac{\sin \theta}{\cos \theta}.
Find the value of \tan \theta.
Does \tan \theta = \dfrac{\sin \theta}{\cos \theta}?
George makes the comment that if two angles add to 90 \degree then the sine of one angle is equal to the cosine of the other angle.
Is George correct? Explain your answer.