Tangent = Opposite / Adjacent

The tangent of an angle x is defined as

Use the definition of the tangent and plug in the values given:

tangent C = Opposite / Adjacent = AB / BC = 3 / 7

Therefore, BC = 7.

\(\displaystyle Sine = \frac{opposite}{hypotenuse}. \;Cosine = \frac{adjacent}{hypotenuse}. \;Tangent = \frac{opposite}{adjacent}\)

The cosine of the angle is \(\displaystyle 5/12\) and since that is a reduced fraction, we know the hypotenuse is \(\displaystyle 12\) and the adjacent side equals \(\displaystyle 5\).  

The sine of the angle equals \(\displaystyle 2/3\), and since the hyptenuse is already \(\displaystyle 12\) we know that we must multiply the numerator and denominator by \(\displaystyle 4\) to get the common denominator of \(\displaystyle 12\).  Therefore, the opposite side equals \(\displaystyle 8\).  

Since \(\displaystyle tangent = \frac{opposite}{adjacent},\), the answer is \(\displaystyle 8/5\). 

With right triangles, we can use SOH CAH TOA to solve for unknown side lengths and angles. For this problem, we are given the opposite and adjacent sides of the triangle with relation to the angle. With this information, we can use the tangent function to find the angle.

\(\displaystyle \tan = \frac{opposite}{adjacent}\)

\(\displaystyle \tan\left ( \theta\right ) = \frac{21}{8} = 2.63\)

\(\displaystyle \arctan\left ( 2.63\right ) = \theta\)

\(\displaystyle 69.1^{\circ}= \theta\)

With right triangles, we can use SOH CAH TOA to solve for unknown side lengths and angles. For this problem, we are given the opposite and adjacent sides of the triangle with relation to the angle. With this information, we can use the tangent function to find the angle.

\(\displaystyle \tan = \frac{opposite}{adjacent}\)

\(\displaystyle \tan\left ( \theta\right ) = \frac{4}{7} = 0.57\)

\(\displaystyle \arctan\left ( 0.57\right ) = \theta\)

\(\displaystyle 29.7^{\circ}= \theta\)

With right triangles, we can use SOH CAH TOA to solve for unknown side lengths and angles. For this problem, we are given the opposite and adjacent sides of the triangle with relation to the angle. With this information, we can use the tangent function to find the angle.

\(\displaystyle \tan = \frac{opposite}{adjacent}\)

\(\displaystyle \tan\left ( \theta\right ) = \frac{14}{28} = 0.5\)

\(\displaystyle \arctan\left (0.5\right ) = \theta\)

\(\displaystyle 26.6^{\circ}= \theta\)

You can draw your scenario using the following right triangle:

Recall that the tangent of an angle is equal to the ratio of the opposite side to the adjacent side of the triangle. You can solve for the angle by using an inverse tangent function:

\(\displaystyle \small \Theta = tan^-^1(\frac{23}{47})=26.07535558394878\) or \(\displaystyle 26.08$^{\circ}$\).

Recall that the tangent of an angle is equal to the ratio of the opposite side to the adjacent side of the triangle. You can solve for the angle by using an inverse tangent function:

\(\displaystyle \small \Theta = tan^-^1(\frac{45}{27})=59.03624346792652\) or \(\displaystyle 59.04$^{\circ}$\).

First, solve for side MN. Tan(30^°) = MN/16√3, so MN = tan(30^°)(16√3) = 16. Triangle LMN and MNO are similar as they're both 30-60-90 triangles, so we can set up the proportion LM/MN = MN/NO or 16√3/16 = 16/x. Solving for x, we get 9.24, so the closest whole number is 9.