Question

Help please!!!!!!!!!!!!!!

Answer 1

Hello!

The answer is:

$Sin(u)=0.86\\Cos(u)=0.50\\Tan(u)=1.73$

Why?

Since it's a right triangle, and we have the adjacent and opposite sides size ($\sqrt{37}$), we can solve it using following the next steps:

Tan(u),

We can find the tangent using the following formula:

$tan(u)=\frac{OppositeSide}{AdjacentSide}= \frac{\sqrt{111} }{\sqrt{37}}=\frac{10.54}{6.08}\\tan(u)=1.73$

Sin(u),

To find the sin(u) we need first to find the hypotenuse of the triangle using the Pythagorean Theorem, so:

$c=\sqrt{a^{2}+b^{2}}$

Where:

$c=hypotenuse\\a=FirstTriangleSide\\b=SecondTriangleSide$

Substituting we have:

$hypotenuse=\sqrt{\sqrt{37}^{2}+\sqrt{111}^{2}}$

$hypotenuse=\sqrt{37+111}=\sqrt{148}=12.17$

Then, we can calculate the sin(u) using the following formula:

$Sin(u)\frac{OppositeSide}{Hypotenuse}=\frac{\sqrt{111} }{12.17}=0.86$

Finally, we can calculate the cos(u) by using the following formula:

Cos(u),

$cos(u)=\frac{AdjacentSide}{Hypotenuse}=\frac{\sqrt{37} }{12.17}=0.50$

Hence,

We have that:

$Sin(u)=0.86\\Cos(u)=0.50\\Tan(u)=1.73$

Have a nice day!

Answer 2

Answer:

Part a) $sin(U)=0.87$

Part b) $cos(U)=0.50$

Part c)  $tan(U)=1.73$

Step-by-step explanation:

step 1

we know that

In the right triangle UST

Applying the Pythagoras Theorem

Find the length side UT

$UT^{2}=(\sqrt{37})^{2}+(\sqrt{111})^{2}$

$UT^{2}=37+111$

$UT=\sqrt{148}\ units$

step 2

Find the sin(U)

we know that

The sine of angle U is the opposite side angle U divided by the hypotenuse

$sin(U)=\frac{ST}{UT}$

substitute the values

$sin(U)=\frac{\sqrt{111}}{\sqrt{148}}=0.87$

step 3

Find the cos(U)

we know that

The cosine of angle U is the adjacent side angle U divided by the hypotenuse

$cos(U)=\frac{US}{UT}$

substitute the values

$cos(U)=\frac{\sqrt{37}}{\sqrt{148}}=0.50$

step 4

Find the tan(U)

we know that

The tangent of angle U is the opposite side angle U divided by the adjacent side angle U

$tan(U)=\frac{ST}{US}$

substitute the values

$tan(U)=\frac{\sqrt{111}}{\sqrt{37}}=1.73$