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In this lesson, we will learn how to express trigonometric functions as ratios in right triangles.

Q1:

In the triangle shown, would we call the side labelled π§ the hypotenuse, the adjacent side to angle π , or the side opposite angle π ?

Q2:

In the triangle shown, is the side labelled π¦ adjacent to angle π , opposite angle π , or the hypotenuse?

Q3:

In the figure, which of the following words describe the position of the side labelled π₯ with respect to the angle π ?

Q4:

Find the length of π΅ πΆ giving the answer to two decimal places.

Q5:

Find c o t π΅ given that π΄ π΅ πΆ is a right triangle at πΆ , where π΄ πΆ = 1 2 c m and π΅ πΆ = 9 c m .

Q6:

Find the values of π₯ and π¦ giving the answer to three decimal places.

Q7:

Find the value of s i n c o s π΅ + πΆ .

Q8:

π΄ π΅ πΆ is an isosceles triangle where π΄ π΅ = π΄ πΆ = 1 7 c m and π΅ πΆ = 3 0 c m . Find the value of t a n πΆ π΄ π· given π· lies on the midpoint of π΅ πΆ where ο« π΄ π· β π΅ πΆ .

Q9:

Find the main trigonometric ratios of β π΄ given π΄ π΅ πΆ is a right-angled triangle at π΅ where the ratio between π΄ π΅ and π΄ πΆ is 4 βΆ 5 .

Q10:

Find s i n c o s πΆ πΆ given that π΄ π΅ πΆ is a right-angled triangle at π΅ where π΄ π΅ = 8 c m and π΄ πΆ = 1 7 c m .

Q11:

Q12:

π π π is a right-angled triangle at π , where π π = 1 6 . 5 c m , π π = 2 8 c m , and π π = 3 2 . 5 c m . Find the measure of β π giving the answer to the nearest second.

Q13:

Find the value of s i n c o s π΅ + πΆ , given that π΄ π΅ πΆ is a triangle, where π΄ π΅ = π΄ πΆ = 4 1 c m , π΅ πΆ = 1 8 c m , and ο« π΄ π· is drawn perpendicular to π΅ πΆ intersecting at π· .

Q14:

Find the value of 6 2 5 π΄ π΄ s i n c o s given π΄ π΅ πΆ is a right-angled triangle at π΅ where 7 π΄ β 2 4 = 0 t a n .

Q15:

πΈ is a point inside a square π΄ π΅ πΆ π· with a side length of 48 cm, where π΅ πΈ = πΆ πΈ and π πΈ = 3 0 c m . Find the value of πΎ , given that πΎ ( π β π ) = 1 3 0 c o s s i n .

Q16:

The governor of a city decided to build a new metro station at point between two existing stations at points and . The distance between and is 2.1 km, and the shortest distance between and the library at point is 3.1 km. Find the distance between points and , given that and are orthogonal. Give your answer to two decimal places.

Q17:

For the given figure, find the lengths of π΄ π΅ and π΄ πΆ . Give your solutions to two decimal places.

Q18:

Find 1 β π΄ πΆ t a n s i n , given π΄ π΅ πΆ is a right-angled triangle at π΅ and 7 π΄ β 2 4 = 0 t a n .

Q19:

Find the value of s i n c o s π΄ + π΄ given π΄ π΅ πΆ is a right-angled triangle at π΅ where π΄ π΅ = 2 7 c m and π΅ πΆ = 3 6 c m .

Q20:

Find the value of 2 π π s i n c o s given π π π is a right-angled triangle at π where π π = 1 0 c m and π π = 2 6 c m .

Q21:

Find 1 7 π΅ πΆ πΆ + π΅ t a n c o s s i n c o s ο¨ ο¨ , given that π΄ π΅ πΆ π· is an isosceles trapezium, where π΄ π· β₯ π΅ πΆ , π΄ π· = 8 c m , π΄ π΅ = 1 7 c m , and π΅ πΆ = 2 4 c m .

Q22:

Find the value of c o s c s c t a n π β π π given π β ο π 2 , π ο and s i n π = 3 5 .

Q23:

During a sandstorm, a tree which was growing perpendicular to the ground snapped at a point in its trunk. The top part of the tree fell and hit the ground so that it was 2 metres from the base of the tree. However, at the point of the break, the tree remained connected. The angle the fallen part of the tree made with the horizontal was 5 6 β . Find the original height of the tree giving the answer to the nearest metre.

Q24:

Rupert rests a 6 m ladder against a wall which is perpendicular to the ground. He measures that the base of the ladder is exactly 1.5 m from the base of the wall. Determine the height, β , where the top of the ladder touches the wall, the angle between the base of the ladder and the ground, π , and the angle between the top of the ladder and the wall, π . Give all of your answers accurate to two decimal places.

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