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A <u>triangle</u> is an example of a class of <em>figures</em> referred to as <em>plane shapes</em>. It has <u>three</u> straight <u>sides</u> and <u>three</u> internal <u>angles</u> which sum up to . The <em>measures</em> of the internal <u>angles</u> of the <u>triangle</u> given in the question are A =
, B =
, and C =
.
A <u>triangle</u> is an example of a class of <em>figures</em> referred to as <em>plane shapes</em>. It has <u>three</u> straight <u>sides</u> and <u>three</u> internal <u>angles</u> which sum up to .
Considering the given question, let the <u>sides</u> of the triangle be: a = 6 km, b = 6.5 km, and c = 7 km.
Apply the <em>Cosine rule</em> to have:
=
+
- 2ab Cos C
So that;
=
+
- 2(6 * 6.5) Cos C
49 = 36 + 42.25 - 78Cos C
78 Cos C = 78.25 - 49
= 29.25
Cos C =
= 0.375
C = 0.375
= 67.9757
C =
Apply the <em>Sine rule</em> to determine the <u>value</u> of B,
=
=
SIn B =
= 0.861
B = 0.861
= 59.43
B =
Thus to determine the value of A, we have;
A + B + C =
A + +
=
A = - 127.4
= 52.6
A =
Therefore the <u>sizes</u> of the <em>internal angles</em> of the triangle are: A = , B =
, and C =
.
For more clarifications on applications of the Sine and Cosine rules, visit: brainly.com/question/14660814
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