SAT Math: Practice Questions-Additional topics in math-Right triangle trigonometry

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  \( \bar{BF}\)

Answer/Explanation

Ans:

\(\angle DAB = 90^{\circ}\) is divided by 3 hence each angle = \(30^{\circ}\) 
In triangle ADE
\(tan \theta =\frac{DE}{AD}\) 
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 \(X\)?

Answer/Explanation

Ans: 70

Question

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

  1. \(5\sqrt{3}\)
  2. 10
  3. 15
  4. \(10\sqrt{3}\)
Answer/Explanation

Ans: B

Question

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

Answer/Explanation

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. \(70sin38°\)
Answer/Explanation

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 \(S\)?

Answer/Explanation

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.
Answer/Explanation

Ans: C

Scroll to Top