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.

Advanced 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.

The exact area of the square ABCD is {{}} square units.

Work out the length of CD correct to 1 decimal place.

Work out the perpendicular height of this isosceles triangle, to 1 decimal place.

Given that FE = 12 cm, EH = 19 cm and angle DHE = $$40^\circ$$, calculate the volume of the cuboid ABCDEFGH, to the nearest integer.

$$=(18\sin(28^\circ))^2\times\pi\times18\cos(28^\circ)$$

Match the parts of the cylinder to the correct calculation/answer.

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(1, -10).

Work out the size of the angle, $$x$$, to 1 decimal place.

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

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