Question 1 - you're good to go. It will be pretty similar to the ladder question we explained earlier, just depends on where the 60 degrees is. Find the side with the question mark.
Question 2 - still has me a little stumped. With sides of 6, 8 and 10 it's a right angles triangle - there's a right angle between the 6 and the 8 and the 10 is the hypotenuse (have you done much with pythagoras' theorem? 6,8,10 is a pythagorean triad which means it has whole number sides and is a perfect right angle, 3,4,5 is another)... Can you give me the exact wording of the question? And a description of the diagram if there is one?
Perpendicular height could be either 6 or 8... or if it's the perpendicular height that meets the side of 10 at the base then it's a complicated process of using trig to find the size of one of the angles and then using that angle to determine the height of the triangle. Don't want to go into that if it's one of the more obvious solutions!
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