ACT 1 Geo: Find trigonometric ratios - One Minute Per Question

Welcome to your ACT 1 Geo: Find trigonometric ratios

$Q_{1}:$ A ratio of the lengths of sides of a right triangle is called .......................

tangent

trigonometric Identities

sine

trigonometric ratio

$Q_{2}:$ Number of trigonometric ratios is

$6$

$5$

$4$

$3$

$Q_{3}:$ In a right triangle, let $\theta $ is an acute angle, then $sin\theta =$

$cos \theta $

$csc \theta $

$cos(90- \theta )$

$csc(90- \theta )$

$Q_{4}:$ In the right triangle, find $cos \theta$, if $sin\theta =\frac{2}{3}$?

$\frac{\sqrt{5}}{3}$

$\frac{2}{3}$

$\frac{4}{9}$

$1$

$Q_{5}:$ In the right triangle, if $sin\theta =\frac{1}{2}$, find $tan \theta$?

$3$

$\frac{1}{\sqrt{3}}$

$\frac{-1}{\sqrt{3}}$

$\sqrt{3}$

$Q_{6}:$ In the triangle shown below $AB =BC= 10$ and $AC = 12 $. What is the value of $cos\theta $ ?

$0.4$

$0.6$

$0.8$

$1.2$

$Q_{7}:$ In the triangle shown below $AB =BC= 10$ and $AC = 12 $. What is the value of $cos\theta $ ?

$0.4$

$0.6$

$0.8$

$1.2$

$Q_{8}:$ In the triangle shown below $AB =BC= 10$ and $AC = 12 $. What is the value of $tan\theta $ ?

$\frac{3}{4}$

$\frac{4}{3}$

$\frac{5}{4}$

$\frac{5}{3}$

$Q_{9}:$ In the figures below $y< x < 90$ and $cosx= siny $. If $x=3a-14$ and $y=50-a$, what is the value of $a $?

$16$

$21$

$24$

$27$

$Q_{10}:$ Given the right triangle $ABC$ below, which of the following is equal to $\frac{a}{c}$?

$sin A$

$tan A$

$cos A$

$csc A$

$Q_{11}:$ In the right triangle shown below, if $tan\theta =\frac{3}{4}$, what is $sin\theta$ ?

$\frac{1}{3}$

$\frac{1}{2}$

$\frac{4}{5}$

$\frac{3}{5}$

$Q_{12}:$ In the isosceles right triangle shown below, what is $tan A$?

$s$

$\frac{1}{s}$

$1$

$\frac{s}{\sqrt{2}}$

$Q_{13}:$ In triangle ABC below, $\overline{AC}\perp \overline{ BD}$. Which of the following does not represent the area of triangle $ABC $?

$\frac{1}{2}(AB cosA+BCcosC)(AB cosABD)$

$\frac{1}{2}(AB cosA+BCcosC)(BC sinC)$

$\frac{1}{2}(AB sinABD+BC sinCBD)(AB sinA)$

$\frac{1}{2}(AB sinABD+BC sinCBD)(BC cosC)$

$Q_{14}:$ In triangle $ABC $, the measure of $\sphericalangle C$ is $90$ , $AC = 24 $, and $BC = 10 $. What is the value of $csc A $?

$\frac{5}{13}$

$\frac{13}{5}$

$\frac{4}{7}$

$\frac{7}{4}$

$Q_{15}:$ In the right triangle $ABC$ below, the cosine of $x$ is $\frac{3}{5}$. If $BC = 12 $, what is the length of $AC $?

$9$

$5$

$3$

$15$

$Q_{16}:$ If $sin(5x- 10)= cos(3x+ 16)$, what is the value of $x $?

$10.5$

$11$

$30$

$36.5$

$Q_{17}:$ In the right triangle $ABC$ below, which of the following must be true?

$cos(90-x)=\frac{b}{c}$

$sin(90-x)=\frac{b}{c}$

$tan(90-x)=\frac{b}{c}$

$Q_{18}:$ If $sin\theta=\frac{1}{2}$, then $csc\theta=$

$\frac{1}{2}$

$2$

$\frac{\sqrt{3}{2}$

$\frac{2}{\sqrt{3}$

$Q_{19}:$ In a $45°-45°-90°$ triangle, the lengths of the sides opposite those angles are in the ratio

$2:2:2\sqrt{2}$

$1:2:\sqrt{2}$

$1:1:2\sqrt{2}$

$1:1:1$

$Q_{20}:$ In a $30°-60°-90°$ triangle, the lengths of the sides opposite those angles are in the ratio

$2:\sqrt{3}:2$

$1:\sqrt{3}:2$

$1:\sqrt{3}:1$

$1:2\sqrt{3}:2$

$Q_{21}:$ In the triangle shown below, what is the value of $x $?

$\frac{5\sqrt{3}}{3}$

$3$

$\frac{10}{3}$

$2\sqrt{3}$

$Q_{22}:$ What is the area of the triangle shown below?

$5\sqrt{2}$

$7.5$

$\frac{13\sqrt{3}}{3}$

$\frac{9\sqrt{3}}{2}$

$Q_{23}:$ Two trains depart at the same time from the same terminal, one traveling due north and the other due east, each along a straight track. If the trains travel at the same average speed, which of the following most closely approximates the number of miles each train has traveled when the shortest distance between the two trains is $70$ miles?

$49$

$55$

$60$

$70$

$Q_{24}:$ Which expression can be used to find the length of $\overline{QR}$ in centimeters?

$19cos20$

$19tan20$

$19sin70$

$19tan70$

$Q_{25}:$ If $a = cos \theta$ and $b = sin \theta$, then for all $\theta$, $a^{ 2} + b^{ 2}=$

$0$

$1$

$(cos \theta + sin \theta)^{2}$

$(cos \theta . sin \theta)^{2}$

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