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

In rectangle $ABCD$, $AB=10\,$cm and $BC=6\,$cm. The diagonal $AC$ is drawn. Find the angle $\theta$ between $AC$ and side $AB$.

In triangle $ABC$, $AB=AC=7\,$cm and $BC=8\,$cm. A perpendicular from $A$ meets $BC$ at $D$. Calculate the angle $\angle ABC$ to the nearest degree.

Triangle $ABC$ has sides $AB=10\,$cm, $BC=8\,$cm and $AC=6\,$cm. A perpendicular from $C$ meets $AB$ at $D$. Find $\angle ACD$ to the nearest degree.

In trapezoid $ABCD$, $AD\parallel BC$, $AD=12\,$cm, $BC=6\,$cm, $AB=5\,$cm and $DC=5\,$cm. A perpendicular from $C$ meets $AD$ at $E$. Find $\angle CDE$ to the nearest degree.

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.

In the same cuboid $ABCD.EFGH$ with $AB=6\,$cm, $BC=8\,$cm and $AE=3\,$cm, find the angle between line $EB$ and edge $AB$.

In cuboid $ABCD.EFGH$, the base $ABCD$ has $AB=6\,$cm and $BC=8\,$cm, and the height $AE=3\,$cm. Find the angle between the space diagonal $AG$ and the plane $ABCD$.

Triangle $ABC$ has sides $AB=9\,$cm, $AC=12\,$cm and $BC=15\,$cm. A perpendicular from $A$ meets $BC$ at $D$. Calculate the angle $\angle BAD$ to the nearest degree.

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 front face, to the nearest degree.

In triangle $ABC$, $AB=11\,$cm, $BC=13\,$cm, $AC=10\,$cm. A perpendicular from $A$ meets $BC$ at $D$. Find $\angle ADC$ to the nearest degree.

In a cuboid $ABCD.EFGH$, $AB=6\,$cm, $BC=8\,$cm and $AE=3\,$cm. Point $M$ is the midpoint of face $EFGH$. Find the angle between line $AM$ and edge $AE$.