Geometry Right Triangle Trigonometry Test with Point Values (PDF)

Geometry math test: Right Triangle Trigonometry – Maths PDF

Cover of the book Geometry Math Tests with Answer Keys (PDF)

Download as a PDFThe Geometry tests book with answer keysPrintable PDFSee the book ›

Sommaire

This right triangles test for Geometry covers right triangle trigonometry (Common Core G-SRT.C.6, G-SRT.C.7, G-SRT.C.8), with a free PDF to print.

This 45-minute test checks right triangle trigonometry and its applications. It has 9 questions worth 20 points in total. Show every step of the work, label diagrams, and include units where they apply. Calculators are allowed unless the teacher says otherwise.

Time and points

About this test

Grade: Geometry
Chapter: Right Triangle Trigonometry
Standards: G-SRT.C.6, G-SRT.C.7, G-SRT.C.8
Time: 45 minutes
Total: 20 points

Right triangles test: questions

Question 1 – Find a side [2 pts]

Right triangle.

Find x to the nearest tenth.

Question 2 – Find an angle [2 pts]

Legs 9 and 14.

Find the measure of angle A to the nearest tenth of a degree.

Question 3 – Three ratios [3 pts]

A right triangle has legs 20 and 21. (a) Find the hypotenuse. (b) Find the sine, cosine and tangent of the angle opposite the leg of length 20, as fractions.

Question 4 – Complementary [2 pts]

If \(\text{sin}\,A = \frac{8}{17}\) for an acute angle A, find \(\text{cos}\,(90^{\circ} – A)\) and \(\text{cos}\,A\).

Question 5 – Cliff height [2 pts]

Boat and cliff.

From a boat 120 feet from the base of a cliff, the angle of elevation to the top of the cliff is \(35^{\circ}\). Find the height of the cliff to the nearest foot.

Question 6 – Solve a right triangle [3 pts]

Solve the right triangle with hypotenuse 30 and an acute angle of 65°. Find the other angle and both legs to the nearest tenth.

Question 7 – Special triangle [2 pts]

A 45-45-90 triangle has a hypotenuse of 16. Find the length of each leg in simplest radical form.

Question 8 – Depression [2 pts]

From a cliff 60 feet above the sea, the angle of depression to a buoy is 8°. Find the distance from the base of the cliff to the buoy to the nearest foot.

Question 9 – Ramp [2 pts]

A loading ramp is 15 feet long and rises 4 feet. Find the angle it makes with the ground to the nearest tenth of a degree.

Key facts behind this right triangles test

Key facts

sin A = opposite/hypotenuse, cos A = adjacent/hypotenuse, tan A = opposite/adjacent.
sin A = cos (90 degrees minus A) for the acute angles of a right triangle.
Use an inverse function (sin^-1, cos^-1, tan^-1) to find an angle.
Solving a right triangle means finding all sides and acute angles.
Angles of elevation and depression are measured from the horizontal.

How to use this right triangles test

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

All Geometry chapters: Geometry math.

Voter.. post

Free printable PDF