Trigonometric functions are commonly defined as ratios of two sides of a right-angled triangle for a given angle.

The sine of an angle (sin(θ°)) is the y-coordinate of point P on the triangle formed inside the unit circle.

The cosine of an angle (cos(θ°)) is the x-coordinate of point P on the triangle formed inside the unit circle.

The tangent of an angle (tan(θ°)) is the y-coordinate of point Q on the triangle which extends from the unit circle.

Problem solving with right-angled trigonometry

Maths

In this unit, pupils have explored the trigonometric ratios for right-angled triangles in a variety of situations. In the future unit, pupils explore what can be done when we have a triangle that is not right-angled.

In the prior unit, pupils were introduced to the trigonometric ratios and developed the skills to ascertain which ratio would be appropriate for a given problem. In this unit, pupils are introduced to a variety of situations where this knowledge is required, such as 3-D problems and elevation/depression.

Right-angled trigonometry

ABCD is a square on a grid, where each square is 1 unit. Work out the length of BC, to 1 decimal place.

$$7^2-4\times\left(\frac{2\times5}{2}\right)$$

$$4\times\left(\frac{2\times5}{2}\right)-7^2$$

Which of these calculations are correct for finding the area of the square ABCD?

Match the edge with the correct calculation.

Given that this is an isosceles triangle, calculate the angle marked $$x$$ to 1 decimal place.

The area of this isosceles triangle is {{}} $$\text{cm}^2$$ to 3 significant figures.

Given that AB is the diameter of the circle, the area of the circle is {{}} $$\text{cm}^2$$ to 3 significant figures.

Work out the length of the hypotenuse, to 1 decimal place.

Work out the length of the missing side of this right-angled triangle, to 1 decimal place.

Work out the length of the line segment AB, where A(2, 6) and B(5, 10).

Work out $$x$$ to 1 decimal place using the tangent ratio.

Work out the length of the edge marked $$x$$ to 1 decimal place.

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