# Digital SAT Math : Right triangles and trigonometry – Practice Questions

## SAT MAth Practice questions – all topics

• Geometry and Trigonometry Weightage: 15% Questions: 5-7
• Area and volume
• Lines, angles, and triangles
• Right triangles and trigonometry
• Circles

## SAT MAth and English  – full syllabus practice tests

[Calc]  Question  Easy

In the figure shown, right triangle $A B C$ is similar to right triangle $E D C$, where $\angle A C B$ is congruent to $\angle E C D$ and $A E=15$. What is the length of $\overline{C E}$ ?
А) 4
B) 5
C) 8
D) 10

D

### Question

In rectangle $$ABCD$$ above $$E$$ is on \bar{DC}, $$F$$ is on $$\bar{BC} , DE = 6$$  and  $$FC =1$$ .

If angle A is trisected (divided into three equal angles) by  $$\bar{AE}$$  and $$\bar{AF},$$  what is the length of  $$\bar{BF}$$

Ans:

$$\angle DAB = 90^{\circ}$$ is divided by 3 hence each angle = $$30^{\circ}$$
$$tan \theta =\frac{DE}{AD}$$
or
$$tan 30^{\circ} =\frac{6}{AD}$$
or
$$\frac{1}{\sqrt{3}}=\frac{6}{AD}$$
$$AD= 6\sqrt{3}$$
Now
$$BC = BF+FC$$
Hence
$$BF=BC-FC =AD-Fc as AD=BC$$
$$= 6\sqrt{3}-1$$

### Question

In right triangle $$XYZ$$, $$sinx = cos 20°$$. What is the measure, in degrees, of angle $$X$$?

Ans: 70

### Question

What is the length of side AC in the triangle below?

1. $$5\sqrt{3}$$
2. 10
3. 15
4. $$10\sqrt{3}$$

Ans: B

### Question

Triangle ABC is similar to triangle DEF, where angle $$A$$ corresponds to angle $$D$$. What is the value of cos $$F$$?

Ans: 4/5, .8

### Question

In the right triangle PQR, the length of side $\overline{PQ}$ is 70, the measure of angle $$P$$ is 90°, and the measure of angle $$R$$ is 38°. Which of the following represents the length of side $\overline{QR}$

1. $$\frac{70}{sin52°}$$
2. $$\frac{70}{sin38°}$$
3. $$70sin52°$$
4. $$70sin38°$$

Ans: B

### Question

In the triangle RST, angle $$T$$ measures 40 degrees and angle $$R$$ measures 20 degrees. What is the measure, in degrees, of angle $$S$$?

Ans: 120

### Question

Triangles ABC and DEF each have a corresponding angle measuring 40°. Which additional piece of information is sufficient to determine whether these two triangles are similar?

1. The length of line segment AC
2. The length of line segment DE
3. The measure of another pair of corresponding angles in the two triangles.
4. The lengths of one pair of corresponding sides in the two triangles.

Ans: C

Question

What is the volume, in cubic units, of the right triangular prism shown?

1. 22
2. 60
3. 180
4. 360

C

Question

In triangle $A B C$, the measure of angle $A$ is $50^{\circ}$. If triangle $A B C$ is isosceles, which of the following is NOT a possible measure of angle $B$ ?
A. $50^{\circ}$
B. $65^{\circ}$
C. $80^{\circ}$
D. $100^{\circ}$