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?
- \(5\sqrt{3}\)
- 10
- 15
- \(10\sqrt{3}\)
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 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 ?
- \(\frac{70}{sin52°}\)
- \(\frac{70}{sin38°}\)
- \(70sin52°\)
- \(70sin38°\)
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?
- The length of line segment AC
- The length of line segment DE
- The measure of another pair of corresponding angles in the two triangles.
- The lengths of one pair of corresponding sides in the two triangles.
Answer/Explanation
Ans: C