What is x, the straight-line distance from monclova to Durango, to the nearest kilometer? A. 305 km B. 421 km C. 423 km or D. 478 km

The correct answer is option C: 423 km

Step-by-step explanation: The triangle shows two sides given as 160km and 450km. However the angles facing those sides are yet unknown. Also the third side is unknown (marked x) but the angle facing line x is given as 70 degrees. These dimensions satisfies the requirements for applying the Cosine Rule which states that;

c^2 = a^2 + b^2 - 2abCosC

In this question we shall take line x to be c, while angle C is 70. Also a and b are 160 and 450 respectively. Hence

x^2 = 160^2 + 450^2 - 2(160 x450) Cos 70

x^2 = 25600 + 202500 - 2(72000) x 0.3420

x^2 = 228100 - (144000 x 0.3420)

x^2 = 228100 - 49249

x^2 = 178852

Add the square root sign to both sides of the equation

x = 422.908

Approximately to the nearest kilometer,

x = 423 km

The straight line distance from Monclova to Durango is 423 kilometers

answer

a,b, and d

explanation

a reflection angle is more than

but less than;

an angle that measures

is a reflex angle.(true)

an angle that measures less than

is acute.(true)

provided we are considering angles greater or equal to zero.

an acute angle lies in the range.

an obtuse angle is less than 180° but more than 90°

an angle that measures 300° is obtuse (false)

an angle that measures 65° is an acute angle.(true)