Exercises for Question Type 7: Working with sine, cosine and area of triangle rule all together

Exercises for Question Type 7: Working with sine, cosine and area of triangle rule all together - IB

Written by official IB examiners

Question 1

Skill question

Geometry and trigonometry

In cuboid $A B C D . E F G H$ , the base $A B C D$ has $A B = 6 cm$ and $B C = 8 cm$ , and the height $A E = 3 cm$ . Find the angle between the space diagonal $A G$ and the plane $A B C D$ .

[4]

Question 2

Skill question

A cuboid has length $9$ cm, width $4$ cm and height $12$ cm. Find the angle between its body diagonal and the diagonal of the base, to the nearest degree.

[3]

Question 3

Skill question

In triangle $A B C$ , $A B = 11 cm$ , $B C = 13 cm$ , and $A C = 10 cm$ . A perpendicular from $A$ meets $[B C]$ at $D$ .

Find $∠ A C D$ to the nearest degree.

[5]

Question 4

Skill question

In trapezoid $A B C D$ , $A D ∥ B C$ , $A D = 12$ cm, $B C = 6$ cm, $A B = 5$ cm and $D C = 5$ cm. A perpendicular from $C$ meets $A D$ at $E$ . Find $∠ C D E$ to the nearest degree.

[4]

Question 5

Skill question

In a cuboid $A B C D . E F G H$ , $A B = 6$ cm, $B C = 8$ cm and $A E = 3$ cm. Point $M$ is the midpoint of face $E F G H$ . Find the angle between line $A M$ and edge $A E$ .

[6]

Question 6

Skill question

In triangle $A B C$ , $A B = A C = 7$ cm and $B C = 8$ cm. A perpendicular from $A$ meets $B C$ at $D$ . Calculate the angle $∠ A B C$ to the nearest degree.

[3]

Question 7

Skill question

A cuboid has length $5$ cm, width $12$ cm and height $2$ cm. Find the angle between the space diagonal and a diagonal of its base, to the nearest degree.

[3]

Question 8

Skill question

Triangle $A B C$ has sides $A B = 15$ cm, $A C = 13$ cm and $B C = 14$ cm. A perpendicular from $A$ meets $B C$ at $D$ . Calculate the size of angle $B A D$ to the nearest degree.

[8]

Question 9

Skill question

In rectangle $A B C D$ , $A B = 10 cm$ and $B C = 6 cm$ . The diagonal $A C$ is drawn.

Find the angle $θ$ between $A C$ and side $A B$ .

[2]

Question 10

Skill question

In cuboid $A B C D . E F G H$ with $A B = 6 cm$ , $B C = 8 cm$ and $A E = 3 cm$ , find the angle between line $E B$ and edge $A B$ .

[2]

Question 11

Skill question

The question involves properties of triangles, including calculating area, finding the length of an altitude, and using trigonometric ratios to find an unknown angle.

Triangle $A B C$ has sides $A B = 10 cm$ , $B C = 8 cm$ and $A C = 6 cm$ . A perpendicular from $C$ meets $A B$ at $D$ . Find $∠ A C D$ to the nearest degree.

[7]

IB Mathematics Applications & Interpretation Question Type 7: Working with Sine, Cosine and Area of Triangle Rule All Together Exercises