Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Please verify your account before proceeding.

In this lesson, we will learn how to find an angle in a right triangle using the tangent ratio.

Q1:

Find the values of πΌ and π½ giving your answer to the nearest second.

Q2:

π΄ π΅ πΆ is a right-angled triangle at π΅ , where π΄ π΅ = 4 5 c m and π΅ πΆ = 6 8 c m . Find the measure of β πΆ giving the answer to the nearest second.

Q3:

π΄ π΅ πΆ π· is a rhombus where π΄ πΆ = 2 4 c m and π΅ π· = 3 2 c m . Find π β π΅ π΄ πΆ giving the answer to the nearest second.

Q4:

π΄ π΅ πΆ is a right-angled triangle at π΅ where π΄ π΅ = 1 9 c m and π β πΆ = 5 4 β . Find the length of π΅ πΆ giving the answer to two decimal places.

Q5:

π΄ π΅ πΆ is a triangle where π΄ π· β π΅ πΆ , π β π΅ = 5 1 1 6 β² 1 8 β² β² β , π΅ πΆ = 2 0 c m , and π΄ π· = 8 c m . Find π β πΆ giving the answer to the nearest second.

Q6:

The following figure represents a line segment joining two points π΄ ( 2 , 0 ) and π΅ ( 3 , 8 ) . Find the measure of the angle π included between π΄ π΅ and the π₯ -axis giving the answer to the nearest second.

Q7:

A flagpole 5.9 metres tall casts a 2.8-meter shadow. Find the angle of inclination of the sun giving the answer to the nearest minute.

Q8:

Find the value of πΎ , given π΄ π΅ πΆ is an equilateral triangle, where point π· lies on π΄ π΅ , π΄ π· = 5 c m , π· π΅ = 1 2 c m , and πΎ π = β 3 t a n .

Q9:

Find π₯ to two decimal places.

Q10:

In the given figure, π β π΅ π΄ πΆ = 9 0 β and π΄ π· β₯ π΅ πΆ . What is π΄ πΆ π t a n ?

Q11:

π΄ π΅ πΆ is a right-angled triangle at π΅ , where π΄ π΅ = 6 4 c m . Point π· lies on π΅ πΆ and point πΈ lies on π΄ πΆ where πΈ π· β₯ π΄ π΅ . Find the length of π· π΅ given πΆ π· = 1 2 c m and πΈ π· = 3 5 c m . Give the answer to two decimal places.

Q12:

π΄ π΅ πΆ is a right-angled triangle at π΅ where π β πΆ = 3 4 1 2 β² β and π΅ πΆ = 2 5 c m . Find the length of π΄ π΅ giving the answer to two decimal places.

Q13:

Find the exact value of t a n πΆ .

Q14:

The dimensions of a rectangular garden is 13 metres by 12 metres. Triangle π΄ πΈ πΆ represents the lawn where πΈ πΆ = 1 0 m . Find the measure of β πΈ π΄ π΅ giving the answer to the nearest second.

Q15:

π π π is a triangle where πΏ lies on π π such that π πΏ β π π , t a n t a n π = π π πΏ = 2 0 2 1 and π πΏ = 2 6 c m . Find the area of π π π giving the answer to two decimal places.

Q16:

Find the length of π· πΆ given π΄ π΅ πΆ π· is a quadrilateral where π΄ π· = 6 c m and π΄ π΅ = 8 c m .

Q17:

π΄ π΅ πΆ is a triangle where π΄ π· β π΅ πΆ , π΄ π· = 1 6 c m , π β π΅ = 4 4 β , and π β πΆ = 4 8 β . Find, to the nearest centimetre, the length of π΅ πΆ .

Q18:

In the given figure, π β π΅ π΄ πΆ = 9 0 β where π΄ π· β₯ π΅ πΆ . What is π΄ π· π t a n ?

Q19:

Find the value of t a n t a n π₯ + π¦ given π΄ π΅ πΆ π· is a square where points πΈ and π lie on π΄ πΆ , π΄ πΈ = 8 c m , πΈ π = 2 5 c m , and π πΆ = 9 c m .

Q20:

π΄ π΅ πΆ is a right-angled triangle at π΅ . Point π· lies on π΅ πΆ and point πΈ lies on π΄ πΆ where πΈ π· β₯ π΄ π΅ . Find the area of the trapezium π΄ π΅ π· πΈ given π΄ π΅ = 2 4 c m , πΆ π· = 3 5 c m , and πΈ π· = 1 2 c m . Give the answer to two decimal places.

Q21:

π΄ π΅ πΆ is a right angled triangle at π΅ . Find the area of π΄ π΅ πΆ given that π΄ π΅ = 2 4 c m , π· β π΄ πΆ , πΈ β π΅ πΆ , π· πΈ β π΅ πΆ , and 5 π· πΈ = 6 πΈ πΆ . Round your answer to two decimal places.

Q22:

Find the value of t a n t a n π΅ πΆ given π΄ π΅ πΆ is an isosceles triangle where π΄ π΅ = π΄ πΆ = 4 5 c m and π΅ πΆ = 7 2 c m .

Q23:

π΄ π΅ πΆ is a triangle where π = 1 3 β 3 π and π β πΆ = 1 5 0 β . Find the value of t a n π΄ without using a calculator.

Q24:

In the given figure, the two triangles are similar.

Work out the value of t a n π for β³ π΄ π΅ πΆ . Give your answer as a fraction in its simplest form.

Work out the value of t a n π for β³ π· πΈ πΉ . Give your answer as a fraction in its simplest form.

What can be said about the value of t a n π for two similar triangles?

Q25:

π΄ π΅ is a diametre of a circle with radius 17 cm. Point πΆ is on the circumference of the circle where π΄ πΆ β₯ πΆ π΅ and π΄ πΆ = 1 6 c m . Find the exact values of t a n π΄ and t a n π΅ .

Donβt have an account? Sign Up