Question

solve the problem using the pythagorean theom i think and sides given if you do not put a honest answer you will be reported

Answer 1

The value of FH=5.97,GH=5.76, angle F=44

In triangle GHF, where angle GHF is 90 degrees, and GF measures 8.3 units, we want to find the lengths of FH and GH, and the measure of angle HGF.

Using trigonometric ratios, we can solve this right-angled triangle problem.

The measure of angle HGF is given as 46 degrees, so we can use the sine and cosine trigonometric functions to find the lengths of FH and GH, respectively.

For side FH (opposite to the given angle HGF), we use the sine function:

FH = GF * sin(HGF) = 8.3 * sin(46 degrees).

FH=5.97.

For side GH (adjacent to the given angle HGF), we use the cosine function:

GH = GF * cos(HGF) = 8.3 * cos(46 degrees).

GH=5.76

m ∠H + m ∠G + m ∠F=180

90+46 + m ∠F=180

136 + m ∠F=180

m ∠F=180-136

m ∠F=44

Therefore, The measure of angle F is 44 degree

The probable question may be:

In triangle GHF, angle GHF=90 degree, GF=8.3,angle HGF=46 degree.

Find: FH, GH and measure of angle F

Answer 2

`\sf FH = 6.0`

`\sf FH = 6.0`

`\sf \angle F = 44^\circ`

Explanation:

Given:

-
`\sf \triangle GHF`

-
`\sf \angle G = 46^\circ`

-
`\sf \angle H = 90^\circ`

-
`\sf GF = 8.3`

To Find:

-
`\sf FH`

-
`\sf GH`

-
`\sf \angle F`

Solution:

To find
`\sf FH` using
`\sf \sin G = (FH)/(GF)`:

`\sf \sin(\angle G) = (FH)/(GF)`

Given that
`\sf \angle G = 46^\circ`, we can use a calculator to find
`\sf \sin(46^\circ)`. Let's denote this value as
`\sf \sin G`.

`\sf \sin (46^\circ) = (FH)/(8.3)`

Solving for
`\sf FH`:

`\sf FH = 8.3 \cdot \sin (46^\circ)`

`\sf FH = 5.970520343`

`\sf FH = 6.0 \textsf{( in nearest tenth)}`

To find
`\sf GH` using
`\sf \cos G = (GH)/(GF)`:

`\sf \cos(\angle G) = (GH)/(GF)`

Given that
`\sf \angle G = 46^\circ`, we can use a calculator to watchfind
`\sf \cos(46^\circ)`. Let's denote this value as
`\sf \cos G`.

`\sf \cos (46^\circ) = (GH)/(8.3)`

Solving for
`\sf GH`:

`\sf GH = 8.3 \cdot \cos (46^\circ)`

`\sf GH = 5.765664475`

`\sf GH = 5.8 \textsf{( in nearest tenth)}`

3. Find
`\sf \angle F` using the sum of interior angles:

The sum of interior angles in a triangle is
`\sf 180^\circ`. Therefore,

`\sf \angle F +\angle G + \angle H = 180^\circ`

Solve for
`\sf \angle F`

`\sf \angle F = 180^\circ - \angle G - \angle H`

Substitute the known values:

`\sf \angle F = 180^\circ - 46^\circ - 90^\circ`

`\sf \angle F = 44^\circ`

Summary:

`\sf FH = 6.0`

`\sf FH = 6.0`

`\sf \angle F = 44^\circ`