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• Geometry
• Triangles
• Right triangle

# Right triangle

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•  Question 1: 1 pts Which expression is true?
 $\sin \alpha = \dfrac{a}{c}$ $\cos \alpha = \dfrac{a}{c}$ $\tan \alpha = \dfrac{a}{c}$ $\cot \alpha = \dfrac{a}{c}$
•  Question 2: 1 pts The legs of a right triangle $\bigtriangleup \mbox{ABC}$ are $a=6cm, b=8cm.$ Determine size of the hypotenuse $c .$
Hypotenuse $c=$
•  Question 3: 1 pts Find the area of the right triangle shown on the picture.
Area $=$
•  Question 4: 1 pts The area of a right triangle is half the area of the rectangle that would surround it.
•  Question 5: 2 pts Evaluate $\sin 45^{\circ}.$
 $\sqrt{2}$ $\dfrac{1}{2}$ $\dfrac{\sqrt{2}}{2}$ $\dfrac{2}{\sqrt{2}}$
•  Question 6: 2 pts In an isosceles right triangle, the hypotenuse is $\sqrt{10}$ inches. How long are the sides?
The sides will be
•  Question 7: 2 pts Find the measure of the angle indicated.
$\theta =$
•  Question 8: 2 pts Find the measure of the side indicated. Round to the nearest tenth.
$x=$
•  Question 9: 3 pts A ladder $9 m$ long is placed against a building. The angle between the ladder and the ground is $65^{\circ}$ . How high up is the top of the ladder? Present your answer as an exact value, if we denote the height of the top of the ladder by $y.$
 $9 \cdot \cos 25^{\circ}=y$ $9 \cdot \sin 25^{\circ}=y$ $9 \cdot \sin 65^{\circ}=y$ $9 \cdot \cos 65^{\circ}=y$
•  Question 10: 3 pts Carlos is surveying a plot of land in the shape of a right triangle. The area of the land is 45,000 square meters. If one leg of the triangular plot is 180 meters long, the other leg of the triangle is 400 meters long.
•  Question 11: 2 pts $\bigtriangleup ABC$ is a right triangle. The length of its perimeter is equal to $60$ units and the size of its area is equal $150 \mbox{units}^{2}.$ Find its two sides and hypotenuse.
 25 units, 20 units and 15 units. 15 units, 20 units and 25 units. 15 units, 20 units and 15 units. 15 units, 25 units and 20 units.
•  Question 12: 2 pts Find the measure of the angle indicated. Round to the nearest tenth.
$\theta =$