117k views
5 votes
Solve for xx. Round to the nearest tenth, if necessary.​

Solve for xx. Round to the nearest tenth, if necessary.​-example-1
User Quirico
by
6.5k points

2 Answers

1 vote

Answer:

Explanation:

take 58 degree as reference angle

using cos rule

cos 58=adjacent/hypotenuse

0.52=3.6/x

x=3.6/0.52

x=6.92

x=6.9

User Cassio Groh
by
6.4k points
4 votes

The length of the base (IJ) in triangle KIJ, given a height (KJ) of
3.6 units, an angle IKJ of
58 degrees, and a right angle at KJI, is approximately
2.3 units.

To solve for the length of the base (IJ = x) in the right-angled triangle KIJ, we can use the tangent function. The tangent of an angle in a right triangle is defined as the ratio of the length of the opposite side to the length of the adjacent side.

In this case, for angle IKJ (
58 degrees), the tangent function is given by:


\[ \tan(58^\circ) = \frac{{\text{height (KJ)}}}{{\text{base (IJ)}}} \]

Given that KJ =
3.6, we can rearrange the formula to solve for IJ (x):


\[ x = \frac{{\text{height (KJ)}}}{{\tan(\text{angle IKJ})}} \]

Substitute the known values:


\[ x = \frac{{3.6}}{{\tan(58^\circ)}} \]

Now, calculate this expression to find the length of the base IJ = x. Round to the nearest tenth as necessary.


\[ x = \frac{{3.6}}{{\tan(58^\circ)}} \]

Now, let's calculate this expression:


\[ x = \frac{{3.6}}{{\tan(58^\circ)}} \]

Using a calculator:


\[ x \approx \frac{{3.6}}{{1.542}} \]\[ x \approx 2.335 \]

Therefore, the length of the base (IJ) is approximately
2.3 (rounded to the nearest tenth) units.

User Gerhard Schlager
by
6.6k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.