Question

Someone please help with this please

Answer 1

`b = \bf 21 \space\ cm`

Explanation:

• To solve for a side using SOH CAH TOA, first check the angle whose measure is given.

In this case, we know ∠ C is 25°.

• Next we have to figure out the relationships between the given angle and two sides: one side whose length we know, and the other whose length we have to find.

In this case, the side opposite to ∠ C is known to be 10 cm, and the side adjacent to ∠ C is AC, whose length, b, we have to find.

• The trigonometric ratio that relates the adjacent and opposite sides of an angle is tan, where:

`\boxed{tan \theta = (opposite)/(adjacent) }` .

We can use this relationship to calculate the value of b:

⇒
`tan (25 \textdegree) = (10)/(b)`

Solving for b:

⇒
`b \cdot tan (25 \textdegree) = 10`

⇒
`b = (10)/(tan (25 \textdegree))`

⇒
`b = 21.45`

⇒
`b \approx \bf 21 \space\ cm` (rounded to the nearest whole number)

Answer 2

b = 21

Explanation:

In general for these trig problems look for the angle whose measure you are given or need to find and for the sides you are given lengths or whose sides you need to find.

Given:

side AB = 10 cm

m<C = 25°

Find:

side AC

The angle of interest here is <C whose measure is 25°.

Now look at the given side and the side you are looking for with respect to angle C, the given angle.

For angle C, AC is the adjacent leg.

For angle C, AB is the opposite leg.

Which trig function relates the opposite leg to the adjacent leg?

It is the tangent, since, in general, tan X = opp/adj.

tan C = opp/adj

tan 25° = AB/AB

tan 25° = 10 cm/b

Solve for b.

b × tan 25° = 10 cm

b = 10 cm / tan 25°

Using your calculator, divide 10 by the tangent of 25°.

b = 21.44506...

Answer: b = 21