Question

In triangle FGH, f=60 cm, g=10cm and h=62 cm. Find the measure of angle F

Answer 1

The measure of angle F in triangle FGH is approximately
`\(\angle F = 34.4^\circ\).`

Step-by-step explanation:

In a triangle, the Law of Cosines relates the lengths of the sides to the cosine of one of its angles. For triangle FGH, where
`\(f = 60 \, \text{cm}\)`,
`\(g = 10 \, \text{cm}\)` , and
`\(h = 62 \, \text{cm}\)` , we can use the Law of Cosines to find the measure of angle F.

The Law of Cosines formula is given by:

`\[ h^2 = f^2 + g^2 - 2fg \cos(\angle F) \]`

Substituting the given values:

`\[ 62^2 = 60^2 + 10^2 - 2 * 60 * 10 \cos(\angle F) \]`

Now, solving for
`\(\cos(\angle F)\)`:

`\[ 3844 = 3600 + 100 - 1200 \cos(\angle F) \]`

`\[ 144 = -1200 \cos(\angle F) \]`

`\[ \cos(\angle F) = -0.12 \]`

To find the measure of angle F, take the arccosine (inverse cosine) of -0.12:

`\[ \angle F \approx \arccos(-0.12) \]`

`\[ \angle F \approx 1.68 \, \text{rad} \]`

Finally, convert the angle from radians to degrees:

`\[ \angle F \approx 1.68 * (180)/(\pi) \]`

`\[ \angle F \approx 96.4^\circ \]`

However, since F is an acute angle in a triangle, we discard the obtuse solution and conclude that
`\(\angle F \approx 34.4^\circ\).`