# Grade 11 trig help! These three confuse me a lot? Relevance
• 1. The "question" here is unclear at best.

There are two different triangles that satisfy the given conditions because 60<70.

One is where the angle to his right is acute (longer right side) and one when it's obtuse (shorter right side)

So you have sin56° / 60 = sinx / 70

With solutions being x = 75.3° and x = 180 - 75.3°

With the remaining side being 54.4 m and 23.9 m

So I guess the question is can the surveyor know the shape of the field from only the specified measurements. The answer is no, but since the surveyor was kinda THERE when he was doing it, he can determine which of the two options is going on as the triangles are vastly different.

When the two choices are more similar e.g. the angle being 85° or 95° then that probably can't be eyeballed.

2.

Draw diagram. The relevant angles in the triangle are 60° and 75°

Mark the point where they could possibly collide. The distances they have to travel to get there are in the ratio Bravery / Courageous = sin75° / sin60° = 1.115

But the speeds are in the ratio 25/20 = 1.25

The ratios are similar, but not similar enough for there to be a collision because the triangle is so big and the ships small. For an initial separation of 1 km they might collide.

3.

Cosine theorem says

short diagonal = sqrt(20² + 30² - 2(20)(30)cos80°) cm

long diagonal = sqrt(20² + 30² - 2(20)(30)cos100°) cm

Because 180 - 80 = 100

• Can you please take a clearer image, or type out the questions?

If the partial image above the text is revelant then please include it in its entirety.