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This is one of our many quizzes on Solving for an angle in a right triangle. Click on this to access more such competitive quizzes on Geometry.

Solving for an angle in a right triangle Quiz 2

mathematics

 A person standing at the top of a building looking at his own wife on the ground makes a declination angle of $58^\circ $, what would be the inclination angle made by his wife on the ground looking at his husband. $ \\ $ <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/394e9de1-10a7-4ecc-a760-00c9539efb118952370111758124153.png"/>

 Apply angle sum property to solve the given question.

  $  {\text{Apply angle sum property, In }}\Delta HPW   \\   \Rightarrow 58^\circ  + \angle HWP + 90^\circ  = 180^\circ    \\   \Rightarrow \angle HWP + 148^\circ  = 180^\circ    \\   \Rightarrow \angle HWP = 180^\circ  - 148^\circ    \\   \Rightarrow \angle HWP = 32^\circ    \\  {\text{Hence, angle made by wife on the ground}} = 32^\circ    \\  $

 The value of $x$ in right angled triangle in the given figure is $ \\ $ <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/80f4c8af-bfa4-46e7-81b2-b72d852067b56516300309814875603.png"/>

 Apply angle sum property of the right angled triangle to calculate the value of $x$. 

  $ {\text{Apply angle sum property in }}\Delta ABC   \\   \Rightarrow x + 37^\circ  + 90^\circ  = 180^\circ    \\   \Rightarrow x + 127^\circ  = 180^\circ    \\   \Rightarrow x = 180^\circ  - 127^\circ    \\  {\text{Hence, }}x = 53^\circ    \\  $

 The value of ‘a’ in the given right angled triangle is $ \\ $ <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/31f01851-93c3-4387-88c8-811851db64f57806866992236964750.png"/>

 Apply angle sum property of triangle to calculate the value of $'a'$. 

$  {\text{Apply angle sum property in }}\Delta ABC   \\   \Rightarrow a + a + 90^\circ  = 180^\circ    \\   \Rightarrow 2a + 90^\circ  = 180^\circ    \\   \Rightarrow 2a = 180^\circ  - 90^\circ    \\   \Rightarrow 2a = 90^\circ    \\   \Rightarrow a = \dfrac{{90^\circ }}{2}   \\   \Rightarrow a = 45^\circ    \\  {\text{Hence, }}a = 45^\circ    \\  $

 Considering the given figure, find the value of $k$. $ \\ $ <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/aa1dc60a-738a-479c-9cd5-6da1e9fec9bf5605560104330371585.png"/>

 Apply the angle sum property of a right angled triangle to calculate the value of $'k'$.

 $  {\text{Apply angle sum property of triangle}}   \\   \Rightarrow \dfrac{4}{3}k + \dfrac{3}{5}k + 90^\circ  = 180^\circ    \\   \Rightarrow \dfrac{{20k + 9k}}{{15}} = 90^\circ    \\   \Rightarrow \dfrac{{29k}}{{15}} = 90^\circ    \\   \Rightarrow k = \dfrac{{90 \times 15}}{{29}}   \\ {\text{Hence, }}k = \dfrac{{1350}}{{29}}   \\  $

 Solve for the value of $x$ from the given figure. $ \\ $ <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/2c0de2d8-9c1b-4d4d-8d3b-8c75417eba4a4265336296642601916.png"/>

 Apply the angle sum property of the triangle and take both angles equal to calculate the value of $'x'$. 

 $  {\text{Apply angle sum property of triangle}}   \\   \Rightarrow \dfrac{2}{5}x + \dfrac{2}{5}x + 90^\circ  = 180^\circ    \\   \Rightarrow \dfrac{4}{5}x = 90^\circ    \\   \Rightarrow x = \dfrac{{90 \times 5}}{4}   \\   \Rightarrow x = \dfrac{{450}}{4}   \\  {\text{Hence, }}x = 112.5^\circ    \\  $